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Journal articles on the topic 'Superspace formalism'

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Published: 9 March 2023

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1

Bonora, Loriano, and Rudra Prakash Malik. "BRST and Superfield Formalism—A Review." Universe 7, no. 8 (2021): 280. http://dx.doi.org/10.3390/universe7080280.

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This article, which is a review with substantial original material, is meant to offer a comprehensive description of the superfield representations of BRST and anti-BRST algebras and their applications to some field-theoretic topics. After a review of the superfield formalism for gauge theories, we present the same formalism for gerbes and diffeomorphism invariant theories. The application to diffeomorphisms leads, in particular, to a horizontal Riemannian geometry in the superspace. We then illustrate the application to the description of consistent gauge anomalies and Wess–Zumino terms for which the formalism seems to be particularly tailor-made. The next subject covered is the higher spin YM-like theories and their anomalies. Finally, we show that the BRST superfield formalism applies as well to the N=1 super-YM theories formulated in the supersymmetric superspace, for the two formalisms go along with each other very well.

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2

Lasukov, V. V. "String formalism in superspace-time." Russian Physics Journal 54, no. 7 (2011): 801–13. http://dx.doi.org/10.1007/s11182-011-9687-z.

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3

FAIZAL, MIR. "HARMONIC SUPERSPACE GAUGEON FORMALISM FOR THE ABJM THEORY." Modern Physics Letters A 27, no. 26 (2012): 1250147. http://dx.doi.org/10.1142/s0217732312501477.

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In this paper, we will analyze the ABJM theory in harmonic superspace. The harmonic superspace variables will be parametrized by the coset SU(2)/U(1) and thus will have manifest [Formula: see text] supersymmetry. We will study the quantum gauge transformations and the BRST transformations of this theory in gaugeon formalism. We will use this BRST symmetry to project out the physical subspace from the total Hilbert space. We will also show that the evolution of the [Formula: see text]-matrix is unitary for this ABJM theory in harmonic superspace.

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4

Aratyn, H., C. Rasinariu, and A. Das. "Zero Curvature Formalism for Supersymmetric Integrable Hierarchies in Superspace." Modern Physics Letters A 12, no. 34 (1997): 2623–30. http://dx.doi.org/10.1142/s0217732397002752.

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We generalize the Drinfeld–Sokolov formalism of bosonic integrable hierarchies to superspace, in a way which systematically leads to the zero curvature formulation for the supersymmetric integrable systems starting from the Lax equation in superspace. We use the method of symmetric space as well as the non-Abelian gauge technique to obtain the supersymmetric integrable hierarchies of the AKNS type from the zero curvature condition in superspace with the graded algebras, sl (n+1,n), providing the Hermitian symmetric space structure.

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5

Madsen, Jens Ole, and Eric Ragoucy. "Quantum hamiltonian reduction in superspace formalism." Nuclear Physics B 429, no. 2 (1994): 277–90. http://dx.doi.org/10.1016/0550-3213(94)00258-4.

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6

Sofi, Ashaq Hussain, and Sajad Ul Majeed. "Chern-Simons-Matter Theory in Superspace Formalism." OALib 02, no. 04 (2015): 1–8. http://dx.doi.org/10.4236/oalib.1101421.

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7

Bereciartua, P. J., F. J. Zuñiga, J. M. Perez-Mato, et al. "Structure refinement and superspace description of the system Bi2(n + 2)Mo n O6(n + 1) (n = 3, 4, 5 and 6)." Acta Crystallographica Section B Structural Science 68, no. 4 (2012): 323–40. http://dx.doi.org/10.1107/s0108768112017478.

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The system Bi2(n + 2)Mo n O6(n + 1) is described within the superspace formalism. Two superspace models are proposed for the different members of this family, depending on the parity of the parameter n. The superspace model for the odd members is constructed through the embedding of the cationic distribution of the member with n = 3, and the modification of a superspace model previously proposed for the compound Bi2MoO6. However, this model cannot be applied to the even members of the family. Performing the appropriate transformations, a suitable superspace model for the even members is obtained. The atomic structure of the different compounds of the family have been refined through the Rietveld method combining synchrotron X-ray and neutron powder diffraction data.

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8

McKeon, D. G. C. "Harmonic superspace with four-dimensional Euclidean space." Canadian Journal of Physics 78, no. 4 (2000): 261–66. http://dx.doi.org/10.1139/p00-048.

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The supersymmetry algebra in four-dimensional Euclidean space is formulated in such a way that an SU(2) invariance of the algebra is apparent. This leads to a superfield formalism for representations of the algebra that can be adapted to harmonic superspace. Models in this harmonic superspace are quite similar to N = 2 models in four-dimensional Minkowski space.PACS Nos.: 11.30Pb, 03.65Fd

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9

Ganai, Prince A., Mudasir Ahmad Mir, Ideed Rafiqi, and Nadeem Ul Islam. "Chern–Simons theory in aether superspace." Modern Physics Letters A 32, no. 39 (2017): 1750214. http://dx.doi.org/10.1142/s0217732317502145.

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In this paper, we will analyze the breaking of Lorentz symmetry using aether superspace. We will analyze the aether deformation of a Chern–Simons theory using this deformed superspace. As this theory, will have gauge symmetry, we will add gauge and ghost terms to the original action. We will analyze the nonlinear BRST symmetry for this theory. We also analyze the quantum BRST symmetry in BV formalism.

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10

TAHIRI, M. "UNCONSTRAINED SUPERSPACE FORMALISM OF TOPOLOGICAL 2-D GRAVITY." Modern Physics Letters A 10, no. 26 (1995): 1949–58. http://dx.doi.org/10.1142/s021773239500209x.

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An unconstrained superconnection formalism is used to derive in a natural way the fields and their BRST transformations in topological 2-D gravity. Anti-BRST transformations of the fields are also obtained. We also show how the usual BRST exact quantum action is anti-BRST exact.

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11

MEZIANE, A., and M. TAHIRI. "GEOMETRICAL FORMULATION OF THE BRST TRANSFORMATIONS OF GAUGE-AFFINE GRAVITY." Modern Physics Letters A 11, no. 11 (1996): 885–90. http://dx.doi.org/10.1142/s0217732396000898.

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Fields and their BRST and anti-BRST transformations in gauge-affine gravity are determined by using a superspace formalism. The method is based on the introduction of a basis, instead of the natural one, for differential forms on a (4, 2)-dimensional superspace, whose body is a metric-affine spacetime. This basis is defined after having introduced the coordinate ghost and anti-ghost superfields from a [Formula: see text]-superconnection.

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12

Zhao, Dan, Rong-Hua Zhang, Fei-Fei Li, Juan Yang, Bing-Guo Liu, and Yun-Chang Fan. "(3 + 1)-Dimensional commensurately modulated structure and photoluminescence properties of diborate KSbOB2O5." Dalton Transactions 44, no. 13 (2015): 6277–87. http://dx.doi.org/10.1039/c5dt00267b.

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13

Peral, I., G. Madariaga, V. Petříček, and T. Breczewski. "Average structure of the composite crystal urea/octanedioic acid at room temperature within the superspace formalism." Acta Crystallographica Section B Structural Science 57, no. 3 (2001): 386–93. http://dx.doi.org/10.1107/s0108768101002166.

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The average structure of the composite urea/octanedioic acid has been refined using the superspace formalism [superspace group H′3121(00γ)00\bar{1}]. Modulation effects seem to be almost negligible. The guest substructure appears to be largely disordered and has been modelled using rigid units occupying 12 equiprobable different orientations inside the urea tunnels. Guest molecules are slightly tilted with respect to the tunnel axis favouring a stronger guest–guest intratunnel interaction.

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14

Ganai, Prince A., Owais Ahmad, Javier Perez Tobia, Alexander Fennell, and Vedaant Vyas. "Lorentz symmetry breaking in supersymmetric quantum electrodynamics." International Journal of Geometric Methods in Modern Physics 17, no. 03 (2020): 2050038. http://dx.doi.org/10.1142/s0219887820500383.

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Lorentz symmetry is one of the fundamental symmetries of nature; however, it can be broken by several proposals such as quantum gravity effects, low energy approximations in string theory and dark matter. In this paper, Lorentz symmetry is broken in supersymmetric quantum electrodynamics using aether superspace formalism without breaking any supersymmetry. To break the Lorentz symmetry in three-dimensional quantum electrodynamics, we must use the [Formula: see text] aether superspace. A new constant vector field is introduced and used to deform the deformed generator of supersymmetry. This formalism is required to fix the unphysical degrees of freedom that arise from the quantum gauge transformation required to quantize this theory. By using Yokoyama’s gaugeon formalism, it is possible to study these gaugeon transformations. As a result of the quantum gauge transformation, the supersymmetric algebra gets modified and the theory is invariant under BRST symmetry. These results could aid in the construction of the Gravity’s Rainbow theory and in the study of superconformal field theory. Furthermore, it is demonstrated that different gauges in this deformed supersymmetric quantum electrodynamics can be related to each other using the gaugeon formalism.

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15

Zhao, Dan, Fa-Xue Ma, Rui-Juan Zhang, et al. "Structure modulation, band structure, density of states and luminescent properties of columbite-type ZnNb2O6." CrystEngComm 18, no. 16 (2016): 2929–36. http://dx.doi.org/10.1039/c5ce01828e.

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This study reports the four-dimensional commensurately modulated structure of ZnNb<sub>2</sub>O<sub>6</sub> using superspace formalism for aperiodic structures considering the modulation vector, q = 1/3 b*.

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16

Guevarra, Jonathan, Andreas Schönleber, Sander van Smaalen, and Frank Lichtenberg. "Superspace description of the crystal structures of Ca n (Nb,Ti) n O3n + 2 (n = 5 and 6)." Acta Crystallographica Section B Structural Science 63, no. 2 (2007): 183–89. http://dx.doi.org/10.1107/s0108768107002340.

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The crystal structures of two members of the homologous series Ca n (Nb,Ti) n O3n + 2, with n = 5 and 6, are presented within the superspace formalism. A common (3 + 1)-dimensional superspace model is used to describe the crystal structures of both compositions within a particular homologous series, where the primary modulation wavevector and the width of the atomic domains vary systematically with composition. The two crystal structures are characterized as commensurately modulated structures consisting of discontinuous atomic domains described by occupational crenel functions. The displacive modulation functions for the two compounds exhibit similarities, but they also show that the idea of a unified superspace model does not extend toward the precise atomic positions. For n = 6, the centrosymmetric (3 + 1)-dimensional superspace symmetry provides a natural explanation for the pseudo-symmetries that are present in the non-centrosymmetric (three-dimensional) superstructure of this compound. The efficiency of the superspace approach is demonstrated by structure refinements in (3 + 1)-dimensional superspace and by comparing these results with the refinements in their three-dimensional superstructures.

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17

Kruglov, Sergey I., and Mir Faizal. "Wave function of the universe from a matrix-valued first-order formalism." International Journal of Geometric Methods in Modern Physics 12, no. 04 (2015): 1550050. http://dx.doi.org/10.1142/s0219887815500504.

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In this paper, the Wheeler–DeWitt equation in full superspace formalism will be written in a matrix-valued first-order formalism. We will also analyze the Wheeler–DeWitt equation in minisuperspace approximation using this matrix-valued first-order formalism. We will note that this Wheeler–DeWitt equation, in this minisuperspace approximation, can be expressed as an eigenvalue equation. We will use this fact to analyze the spacetime foam in this formalism. This will be done by constructing a statistical mechanical partition function for the Wheeler–DeWitt equation in this matrix-valued first-order formalism. This will lead to a possible solution for the cosmological constant problem.

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18

Gurzadyan, A. V., and A. A. Kocharyan. "Superspace and global stability in general relativity." International Journal of Modern Physics D 26, no. 05 (2017): 1741019. http://dx.doi.org/10.1142/s021827181741019x.

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A framework is developed enabling the global analysis of the stability of cosmological models using the local geometric characteristics of the infinite-dimensional superspace, i.e. using the generalized Jacobi equation reformulated for pseudo-Riemannian manifolds. We give a direct formalism for dynamical analysis in the superspace, the requisite equation pertinent for stability analysis of the universe by means of generalized covariant and Fermi derivative is derived. Then, the relevant definitions and formulae are retrieved for cosmological models with a scalar field.

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19

Perez, O., and L. Elcoro. "Superspace formalism to crack complex codes in material chemistry." Acta Crystallographica Section A Foundations of Crystallography 64, a1 (2008): C120. http://dx.doi.org/10.1107/s010876730809613x.

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20

Pérez, Olivier. "Superspace formalism: the Swiss army knife of the crystallographer." Acta Crystallographica Section A Foundations of Crystallography 69, a1 (2013): s264. http://dx.doi.org/10.1107/s0108767313097730.

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21

KATO, JUNJI, and AKIKO MIYAKE. "TOPOLOGICAL HYPERMULTIPLET ON N = 2 TWISTED SUPERSPACE IN FOUR DIMENSIONS." Modern Physics Letters A 21, no. 34 (2006): 2569–89. http://dx.doi.org/10.1142/s021773230602161x.

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We propose an N = 2 twisted superspace formalism with a central charge in four dimensions by introducing a Dirac–Kähler twist. Using this formalism, we construct an off-shell twisted hypermultiplet action and find an explicit form of fermionic scalar, vector and tensor transformations. We construct an off-shell Donaldson–Witten theory coupled to the twisted hypermultiplet. We show that this action possesses N = 4 twisted supersymmetry at the on-shell level. It turns out that the four-dimensional Dirac–Kähler twist is equivalent to Marcus' twist.

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22

Mikki, Said. "On the Topological Structure of Nonlocal Continuum Field Theories." Foundations 2, no. 1 (2021): 20–84. http://dx.doi.org/10.3390/foundations2010003.

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An alternative to conventional spacetime is proposed and rigorously formulated for nonlocal continuum field theories through the deployment of a fiber bundle-based superspace extension method. We develop, in increasing complexity, the concept of nonlocality starting from general considerations, going through spatial dispersion, and ending up with a broad formulation that unveils the link between general topology and nonlocality in generic material media. It is shown that nonlocality naturally leads to a Banach (vector) bundle structure serving as an enlarged space (superspace) inside which physical processes, such as the electromagnetic ones, take place. The added structures, essentially fibered spaces, model the topological microdomains of physics-based nonlocality and provide a fine-grained geometrical picture of field–matter interactions in nonlocal metamaterials. We utilize standard techniques in the theory of smooth manifolds to construct the Banach bundle structure by paying careful attention to the relevant physics. The electromagnetic response tensor is then reformulated as a superspace bundle homomorphism and the various tools needed to proceed from the local topology of microdomains to global domains are developed. For concreteness and simplicity, our presentations of both the fundamental theory and the examples given to illustrate the mathematics all emphasize the case of electromagnetic field theory, but the superspace formalism developed here is quite general and can be easily extended to other types of nonlocal continuum field theories. An application to fundamental theory is given, which consists of utilizing the proposed superspace theory of nonlocal metamaterials in order to explain why nonlocal electromagnetic materials often require additional boundary conditions or extra input from microscopic theory relative to local electromagnetism, where in the latter case such extra input is not needed. Real-life case studies quantitatively illustrating the microdomain structure in nonlocal semiconductors are provided. Moreover, in a series of connected appendices, we outline a new broad view of the emerging field of nonlocal electromagnetism in material domains, which, together with the main superspace formalism introduced in the main text, may be considered a new unified general introduction to the physics and methods of nonlocal metamaterials.

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23

Ribeiro, J. L. "Superspace symmetry and phenomenology of incommensurate type-II multiferroics." Acta Crystallographica Section A Foundations and Advances 70, a1 (2014): C515. http://dx.doi.org/10.1107/s2053273314094844.

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The recent upsurge of research work on multiferroic materials has made clear the need for a comprehensive knowledge of the constraints imposed by symmetry on the magnetic structure and tensor properties of incommensurate magnetic phases. That knowledge can be provided by the magnetic superspace formalism in a simple and robust manner. In this communication I will briefly review some of the basic concepts of this formalism pertaining to magnetic systems. Several practical examples will be given in order to illustrate how the assignment of a magnetic superspace group to a given phase is, in general , more restrictive and wide-ranging than the simple assignment of the order parameter irreducible representation. The direct connection between symmetry and phenomenology, which naturally arises via Landau theory, will then be used in order to illustrate how several complex phase diagrams of type-II magneto-electric multiferroics can be interpreted, and how the magnetically induced ferroelectric states can be anticipated on the basis of general symmetry considerations.

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24

KACHKACHI, M., and T. LHALLABI. "N = 2 SUPERCONFORMAL ANOMALIES AND CURVED HARMONIC SUPERSPACE." International Journal of Modern Physics A 07, no. 15 (1992): 3601–21. http://dx.doi.org/10.1142/s0217751x92001605.

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We present the differential geometry formalism of the N = 2 conformal supergravity in harmonic superspace, which allows one to derive the BRST symmetry corresponding to N = 2 super-diffeomorphisms, local Lorentz transformations and local super-Weyl transformations. The extended transgression formula is used and the N = 2 superconformal anomalies are shown.

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25

MATSUDA, SATOSHI, and TSUNEO UEMATSU. "SUPER SCHWARZIAN DERIVATIVES IN N = 4 SU(2)-EXTENDED SUPERCONFORMAL ALGEBRAS." Modern Physics Letters A 05, no. 11 (1990): 841–51. http://dx.doi.org/10.1142/s0217732390000937.

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We investigate anomalous terms in finite superconformal transformations in N = 4 SU(2)-extended superconformal algebras (SCA). Based on the superspace formalism we obtain super Schwarzian derivatives for the N = 4 SCA. Solutions for global superconformal transformations with the vanishing super-Schwarzian derivatives are given.

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26

DAS, ASHOK, and JNANADEVA MAHARANA. "DUALITY OF THE SUPERSTRING IN SUPERSPACE." Modern Physics Letters A 09, no. 15 (1994): 1361–68. http://dx.doi.org/10.1142/s0217732394001180.

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The evolution of a closed NSR string is considered in the background of constant graviton and antisymmetric fields. The σ-model action is written in a manifestly supersymmetric form in terms of superfields. The first order formalism adopted for the closed bosonic string is generalized to implement duality transformations and the constant dual backgrounds are obtained for the dual theory. We recover the G→G−1 duality for the case when antisymmetric tensor field is set to zero. Next, the case when the backgrounds depend on one superfield, is also analyzed. This scenario is similar to the cosmological case envisaged for the bosonic string. The explicit form of the duality transformation is given for this case.

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27

AIDAOUI, A., and M. TAHIRI. "SUPERCONNECTION FORMALISM FOR QUANTIZED BF THEORIES ON BRST–VSUSY SUPERSPACE." International Journal of Geometric Methods in Modern Physics 07, no. 08 (2010): 1321–30. http://dx.doi.org/10.1142/s0219887810004828.

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The arbitrary dimensional BF theory is presented in a superconnection formalism. This makes the off-shell BRST-VSUSY superalgebra more obvious. We also discuss how to build the BRST–VSUSY exact quantum action.

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28

Urcelay-Olabarria, Irene, Juan Manuel Perez-Mato, José Luis García Muñoz, and Eric Ressouche. "Sheding light on the multiferroicity in Mn1-xCoxWO4using superspace formalism." Acta Crystallographica Section A Foundations and Advances 70, a1 (2014): C519. http://dx.doi.org/10.1107/s2053273314094807.

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The use of the superspace symmetry formalism allows to rationalize the physical properties induced by an incommensurate magnetic ordering [1]. The incommensurate magnetic structures (ICMS) in Mn1-xCoxWO4 have been studied in the light of this formalism. MnWO4 is a multiferroic material in which the magnetic order of one of its magnetic phases induces ferroelectricity. Like most multiferroic materials MnWO4 is extremely sensitive to small perturbations such as chemical substitution. It turned out that doping with Co2+ is particularly interesting since it strongly stabilizes the multiferroic phase at low temperatures, and moreover, by increasing the cobalt amount in the crystals the orientation of the electric polarization flops from the b axis to the ac plane [2]. This change of orientation is linked to a symmetry change. The ICMS of the x = 0 and x = 0.10 compounds, which exhibit completely different behavior, have been studied thoroughly using superspace formalism. We have found, not only the symmetry of the magnetic structures and their intrinsic restrictions, but also information about the tensor properties of each incommensurate phase, such as ferroelectric and magnetostructural properties [3]: in the paramagnetic state, there is a unique independent magnetic atom in the crystallographic unit cell in both cases, but when the system enters into the multiferroic phase, this is no-longer true. In the multiferroic phase of MnWO4, the two Mn atoms in the unit cell become symmetry independent, whereas in the x = 0.10 substituted compound, they are still symmetry-related. This difference is related to the change of the electric polarization.

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29

Tahiri, M. "Super and anti-super BF systems in the superspace formalism." Classical and Quantum Gravity 13, no. 6 (1996): 1323–32. http://dx.doi.org/10.1088/0264-9381/13/6/007.

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30

Howe, P. S., and U. Lindström. "Local supertwistors and conformal supergravity in six dimensions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2243 (2020): 20200683. http://dx.doi.org/10.1098/rspa.2020.0683.

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The local supertwistor formalism, which involves a superconformal connection acting on the bundle of such objects over superspace, is used to investigate superconformal geometry in six dimensions. The geometry corresponding to (1, 0) and (2, 0) off-shell conformal supergravity multiplets, as well the associated finite super-Weyl transformations, are derived.

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31

BUCHBINDER, IOSEPH L., and SERGEI M. KUZENKO. "COMMENTS ON THE BACKGROUND FIELD METHOD IN HARMONIC SUPERSPACE: NON-HOLOMORPHIC CORRECTIONS IN N=4 SYM." Modern Physics Letters A 13, no. 20 (1998): 1623–35. http://dx.doi.org/10.1142/s0217732398001704.

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We analyze the one-loop effective action of N=4 SYM theory in the framework of the bakground field formalism in N=2 harmonic superspace. For the case of onshell background N=2 vector multiplet we prove that the effective action is free of harmonic singularities. When the lowest N=1 superspace component of the N=2 vector multiplet is switched off, the effective action of N=4 SYM theory is shown to coincide with obtained by Grisaru et al. on the base of the N=1 background field method. We compute the leading non-holomorphic corrections to the N=4 SU (2) SYM effective action.

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32

Gallego, Samuel V., J. Manuel Perez-Mato, Luis Elcoro, et al. "MAGNDATA: towards a database of magnetic structures. II. The incommensurate case." Journal of Applied Crystallography 49, no. 6 (2016): 1941–56. http://dx.doi.org/10.1107/s1600576716015491.

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A free web page under the nameMAGNDATA, which provides detailed quantitative information on more than 400 published magnetic structures, has been made available at the Bilbao Crystallographic Server (http://www.cryst.ehu.es). It includes both commensurate and incommensurate structures. In the first article in this series, the information available on commensurate magnetic structures was presented [Gallego, Perez-Mato, Elcoro, Tasci, Hanson, Momma, Aroyo & Madariaga (2016).J. Appl. Cryst.49, 1750–1776]. In this second article, the subset of the database devoted to incommensurate magnetic structures is discussed. These structures are described using magnetic superspace groups,i.e.a direct extension of the non-magnetic superspace groups, which is the standard approach in the description of aperiodic crystals. The use of magnetic superspace symmetry ensures a robust and unambiguous description of both atomic positions and magnetic moments within a common unique formalism. The point-group symmetry of each structure is derived from its magnetic superspace group, and any macroscopic tensor property of interest governed by this point-group symmetry can be retrieved through direct links to other programs of the Bilbao Crystallographic Server. The fact that incommensurate magnetic structures are often reported with ambiguous or incomplete information has made it impossible to include in this collection a good number of the published structures which were initially considered. However, as a proof of concept, the published data of about 30 structures have been re-interpreted and transformed, and together with ten structures where the superspace formalism was directly employed, they form this section ofMAGNDATA. The relevant symmetry of most of the structures could be identified with an epikernel or isotropy subgroup of one irreducible representation of the space group of the parent phase, but in some cases several irreducible representations are active. Any entry of the collection can be visualized using the online tools available on the Bilbao server or can be retrieved as a magCIF file, a file format under development by the International Union of Crystallography. These CIF-like files are supported by visualization programs likeJmoland by analysis programs likeJANAandISODISTORT.

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Lourenço, J. A., J. A. Helayël Neto, and W. Spalenza. "Topological Gravity on (D,N)-Shift Superspace Formulation." Advances in High Energy Physics 2018 (August 1, 2018): 1–8. http://dx.doi.org/10.1155/2018/2786081.

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We reassess the subject of topological gravity by following the shift supersymmetry formalism. The gauge-fixing of the theory goes under the Batalin-Vilkovisky (BV) prescription based on a diagram that contains both ghost and antighost superfields, associated with the supervielbein and the super-Lorentz connection. We extend the formulation of the topological gravity action to an arbitrary number of dimensions of the shift superspace by adopting a formulation based on the gauge-fixing for BF-type models.

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Onoda, Mitsuko, Ying Shi, A. Leithe-Jasper, and Takaho Tanaka. "Structure refinement of the layered composite crystal Sc2B1.1C3.2 in a five-dimensional formalism." Acta Crystallographica Section B Structural Science 57, no. 4 (2001): 449–57. http://dx.doi.org/10.1107/s0108768101006607.

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The crystal structure of a layered compound Sc2B1.1C3.2, scandium boride carbide (M r = 140.43), has been re-refined as a commensurate composite crystal using 1795 single-crystal X-ray diffraction intensities with I > 2\sigma(I) collected by Shi, Leithe-Jasper, Bourgeois, Bando & Tanaka [(1999), J. Solid State Chem. 148, 442–449]. The crystal is composed of two layered subsystem structures, i.e. Sc—C—Sc sandwiches and graphite-like layers of the composition B1/3C2/3. The structure refinement was performed in a five-dimensional formalism based on the trigonal superspace group P\bar{3}m1(p00)(0p0)0m0. The unit cell and other crystal data are a = b = 3.387 (1), c = 6.703 (2) Å, V = 66.59 (1) Å3, \boldsigma_{1} = (9/7 0 0), \boldsigma_{2} = (0 9/7 0), Z = 1, D x = 3.501 Mg m−1. Two different three-dimensional sections through the superspace were analyzed, corresponding to two different superstructure models, one with P\bar{3}m1 and the other with P\bar{3}m1. A random distribution of B and C was assumed in the graphite-like layer and 41 structural parameters were introduced. R F /wR F } were 0.0533/0.0482 and 0.0524/0.0476, respectively, for the first and second models. Although the difference between these R F or wR F values was too fine to exclude one of the models definitely, the advantages of using a superspace group were obvious. It not only brought about better convergence of refinement cycles by virtue of fewer parameters, but also gave an insight into the problem of symmetry of the superstructure.

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35

AIDAOUI, A., and M. TAHIRI. "BRST–VSUSY SUPERSPACE AND TWISTED SUPERFIELDS FOR D=4 BF SYSTEMS." Modern Physics Letters A 20, no. 33 (2005): 2567–73. http://dx.doi.org/10.1142/s021773230501769x.

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We propose to construct the off-shell supersymmetric structure present in quantized D=4 BF theories in terms of a BRST–VSUSY superspace formalism. The method is based on the introduction of constrained scalar superfields. We also discuss how to find the D=4 BF action from D=N=4 supersymmetric action by an appropriate twisting process.

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36

BARCELOS-NETO, J., and E. S. CHEB-TERRAB. "SYMPLECTIC QUANTIZATION OF SUPERFIELDS." International Journal of Modern Physics A 09, no. 31 (1994): 5563–81. http://dx.doi.org/10.1142/s0217751x94002272.

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We show how the extension of the Faddeev-Jackiw symplectic quantization (including true constraints) can be used in superspace. We first deal with supersymmetric free field theory in the component language. After that, we consider the method applied to superfields, taken as canonical variables. We also use the formalism, directly in superfield formulation, for the supersymmetric nonlinear sigma model.

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37

DELBOURGO, R., P. D. JARVIS, and G. THOMPSON. "Sp(2) INVARIANT BRST FORMALISM, SUPERSYMMETRY AND WESS-ZUMINO GAUGES." Modern Physics Letters A 01, no. 02 (1986): 95–101. http://dx.doi.org/10.1142/s0217732386000142.

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Covariant quantization of Fermi-Bose supersymmetric gauge theories is formulated within an enlarged superspace (xµ, θα, ξm) with manifest ξ-supertranslation (=extended BRST) and Sp(2) invariance. In Wess-Zumino gauges, the correct ghost and auxiliary field structure emerges by counting arguments for the (N=1) super-Yang-Mills, conformal and Einstein supergravity cases. The super-Yang-Mills case is analyzed in detail for both supercovariant and Wess-Zumino gauge-fixing, with particular emphasis on the Sp(2) assignments of the ghost superfields.

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38

KHELASHVILI, G. A., and V. I. OGIEVETSKY. "NON-RENORMALIZABILITY OF THE MASSIVE N = 2 SUPER-YANG–MILLS THEORY." Modern Physics Letters A 06, no. 23 (1991): 2143–54. http://dx.doi.org/10.1142/s0217732391002335.

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The massive N = 2 supersymmetric Yang–Mills theory is investigated. Its non-renormalizability is revealed starting from the fourth order of the perturbation theory. The N = 2 harmonic superspace approach and the Stueckelberg-like formalism are used. The Stueckelberg fields form some nonlinear sigma model. Non-renormalizability of the latter produces non-renormalizability of the N = 2 supersymmetric Yang–Mills theory.

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39

TANII, YOSHIAKI, and YOSHIYUKI WATABIKI. "VERTEX FUNCTIONS IN THE PATH INTEGRAL FORMALISM OF OPEN STRING THEORIES." International Journal of Modern Physics A 03, no. 11 (1988): 2601–20. http://dx.doi.org/10.1142/s0217751x88001089.

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We study a systematic method to obtain the general vertex functions (of Neveu-Schwarz sector), which are used in the covariant path integral approach to the open bosonic and superstring theories. For the superstring the superspace formulation in the Wess-Zumino gauge is used to construct the vertices at the boundaries of world sheets. For both theories the vertex functions are explicitly obtained for the first four mass levels and coincide with those in the operator formalism.

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40

Christensen, Jeppe, Sven Lidin, Bernard Malaman, and Gerard Venturini. "Vacancy-ordering effects in AlB2-type ErGe2 − x (0.4 < x ≤ 0.5)." Acta Crystallographica Section B Structural Science 64, no. 3 (2008): 272–80. http://dx.doi.org/10.1107/s0108768108005119.

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In the Er–Ge system, the compostion range ErGe2 to Er2Ge3 has been investigated. Eight samples were produced by arc melting of the elements, and analyzed using X-ray powder diffraction. Nine crystal structures were found to be present in the samples. The structures are described as a homologous series and presented within the superspace formalism using the superspace group X2/m(α0γ)0s, X representing the centring vector (½, ½, 0, ½). In this description the modulation vector q = (αa* + γc*) is shown to be a direct measure of the Ge content as ErGe2 − α (α falls in the range 1\over 3 to ½). The large composition range is achieved by extended vacancy ordering in the planar 63 net of Ge with subsequent relaxation.

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41

Braga, Nelson R. F., and Sergio M. de Souza. "Superspace formulation for the Batalin-Vilkovisky formalism with extended BRST invariance." Physical Review D 53, no. 2 (1996): 916–22. http://dx.doi.org/10.1103/physrevd.53.916.

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42

Schoenleber, A., P. Pattison, and G. Chapuis. "Structure and phase transition ofp-chlorobenzamide described in the superspace formalism." Acta Crystallographica Section A Foundations of Crystallography 58, s1 (2002): c183. http://dx.doi.org/10.1107/s0108767302092358.

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43

Izaola, Zunbeltz, Santiago González, Luis Elcoro, J. M. Perez-Mato, Gotzon Madariaga, and Alberto García. "Revision of pyrrhotite structures within a common superspace model." Acta Crystallographica Section B Structural Science 63, no. 5 (2007): 693–702. http://dx.doi.org/10.1107/s0108768107037275.

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The structure of pyrrhotite (Fe1 − x S with 0.05 ≤ x ≤ 0.125) has been reinvestigated in the framework of the superspace formalism. A common model with a centrosymmetric superspace group is proposed for the whole family. The atomic domains in the internal space representing the Fe atoms are parametrized as crenel functions that fulfil the closeness condition. The proposed model explains the x-dependent space groups observed and the basic features of the structures reported up to now. Our model yields for any x value a well defined ordered distribution of Fe vacancies in contrast to some of the structural models proposed in the literature. A new (3 + 1)-dimensional refinement of Fe0.91S using the deposited dataset [Yamamoto & Nakazawa (1982). Acta Cryst. A38, 79–86] has been performed as a benchmark of the model. The consistency of the proposed superspace symmetry and its validity for other compositions has been further checked by means of ab initio calculations of both atomic forces and equilibrium atomic positions in non-relaxed and relaxed structures, respectively.

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44

Ullah, Farman, Prince A. Ganai, Cheralan P. Haritha, and Barilang Mawlong. "Super-Yang–Mills theory on a Lorentz breaking background." International Journal of Geometric Methods in Modern Physics 15, no. 08 (2018): 1850127. http://dx.doi.org/10.1142/s021988781850127x.

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In this paper, we will analyze a super-Yang–Mills Theory on a Lorentz breaking background. This theory will be analyzed using aether superspace formalism. We will also study the quantum symmetries of this theory. Thus, we will analyze this theory both in linear and nonlinear gauges. We will also study the effects of adding a bare mass term in the Curci–Ferrari gauge.

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45

Elcoro, L., J. M. Perez-Mato, and R. L. Withers. "Intergrowth polytypoids as modulated structures: a superspace description of the Sr n (Nb,Ti) n O3n + 2 compound series." Acta Crystallographica Section B Structural Science 57, no. 4 (2001): 471–84. http://dx.doi.org/10.1107/s0108768101005444.

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A new, unified superspace approach to the structural characterization of the perovskite-related Sr n (Nb,Ti) n O3n + 2 compound series, strontium niobium/titanium oxide, is presented. To a first approximation, the structure of any member of this compound series can be described in terms of the stacking of (110)-bounded perovskite slabs, the number of atomic layers in a single perovskite slab varying systematically with composition. The various composition-dependent layer-stacking sequences can be interpreted in terms of the structural modulation of a common underlying average structure. The average interlayer separation distance is directly related to the average structure periodicity along the layer stacking direction, while an inherent modulation thereof is produced by the presence of different types of layers (particularly vacant layers) along this stacking direction. The fundamental atomic modulation is therefore occupational and can be described by means of crenel (step-like) functions which define occupational atomic domains in the superspace, similarly to what occurs for quasicrystals. While in a standard crystallographic approach, one must describe each structure (in particular the space group and cell parameters) separately for each composition, the proposed superspace model is essentially common to the whole compound series. The superspace symmetry group is unique, while the primary modulation wavevector and the width of some occupation domains vary linearly with composition. For each rational composition, the corresponding conventional three-dimensional space group can be derived from the common superspace group. The resultant possible three-dimensional space groups are in agreement with all the symmetries reported for members of the series. The symmetry-breaking phase transitions with temperature observed in many compounds can be explained in terms of a change in superspace group, again in common for the whole compound series. Inclusion of the incommensurate phases, present in many compounds of the series, lifts the analysis into a five-dimensional superspace. The various four-dimensional superspace groups reported for this incommensurate phase at different compositions are shown to be predictable from a proposed five-dimensional superspace group apparently common to the whole compound series. A comparison with the scarce number of refined structures in this system and the homologous (Nb,Ca)6Ti6O20 compound demonstrates the suitability of the proposed formalism.

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46

Zhang, Rui-Juan, Dan Zhao, Qiu Zhong, Ya-Li Xue, and Guang-Xu Huang. "Na3Sm(PO4)2: (3+1)-dimensional commensurately modulated structure model and photoluminescence properties." Zeitschrift für Kristallographie - Crystalline Materials 234, no. 5 (2019): 281–89. http://dx.doi.org/10.1515/zkri-2018-2095.

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Abstract For the first time, we determined the detailed crystal structure of Na3Sm(PO4)2 using single crystal X-ray diffraction and established the commensurately modulated structure model using the superspace formalism. The structure adopts a (3+1)-dimensional superspace group Pca21(0β0)000 with the modulation vector q=1/3b*. At the same time, the photoluminescent properties of Na3Sm(PO4)2 sintered at different temperatures between 800 and 1200°C were studied. Under near-UV excitation (402 nm), Na3Sm(PO4)2 shows intense characteristic emission bands of Sm3+ (561, 596, 642 nm) with the CIE coordinate of (0.5709, 0.4282), corresponding to orange color. The excitation spectrum covers a wide range from 350 nm to 470 nm, which indicates that Na3Sm(PO4)2 can be efficiently activated by near-UV or visuable LED ship.

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47

THÜMMEL, O. "EXTENDED CONFORMAL SUPERGRAVITY AND BELTRAMI VARIABLES." International Journal of Modern Physics A 09, no. 10 (1994): 1631–75. http://dx.doi.org/10.1142/s0217751x94000716.

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By using a geometric BRST formalism we investigate the two-dimensional N = 2 and N = 4 superspace geometry. The BRST algebra allows one to generalize the notion of Beltrami variables to the extended supergeometries. Furthermore, this geometric treatment yields a systematic way to derive different off-shell supergravities. Finally we construct the Chern–Simons form and calculate from this the superconformal anomaly for the N = 2 and N = 4 theories.

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48

Bhanja, T., N. Srinivas, and R. P. Malik. "Universal Superspace Unitary Operator and Nilpotent (Anti-)Dual-BRST Symmetries: Superfield Formalism." Advances in High Energy Physics 2016 (2016): 1–17. http://dx.doi.org/10.1155/2016/2764245.

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We exploit the key concepts of the augmented version of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the superspace (SUSP)dualunitary operator and its Hermitian conjugate and demonstrate their utility in the derivation of the nilpotent and absolutely anticommuting (anti-)dual-BRST symmetry transformations for a set of interesting models of theAbelian1-form gauge theories. These models are the one (0+1)-dimensional (1D) rigid rotor and modified versions of the two (1+1)-dimensional (2D) Proca as well as anomalous gauge theories and 2D model of a self-dual bosonic field theory. We show theuniversalityof the SUSPdualunitary operator and its Hermitian conjugate in the cases ofallthe Abelian models under consideration. These SUSP dual unitary operators, besides maintaining the explicit group structure, provide the alternatives to the dual horizontality condition (DHC) and dual gauge invariant restrictions (DGIRs) of the superfield formalism. The derivations of thedualunitary operators and corresponding (anti-)dual-BRST symmetries are completelynovelresults in our present investigation.

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49

ILINSKI, K. N., and V. M. UZDIN. "QUANTUM SUPERSPACE, q-EXTENDED SUPERSYMMETRY AND PARASUPERSYMMETRIC QUANTUM MECHANICS." Modern Physics Letters A 08, no. 28 (1993): 2657–70. http://dx.doi.org/10.1142/s0217732393003044.

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We describe q-deformation of the extended supersymmetry and construct q-extended supersymmetric Hamiltonian. For this purpose we formulate q-superspace formalism and construct q-supertransformation group. On this basis q-extended supersymmetric Lagrangian is built. The canonical quantization of this system is considered. The connection with multi-dimensional matrix representations of the parasupersymmetric quantum mechanics is discussed and q-extended supersymmetric harmonic oscillator is considered as a simplest example of the described constructions. We show that extended supersymmetric Hamiltonians obey not only extended SUSY but also the whole family of symmetries (q-extended supersymmetry) which is parametrized by continuous parameter q on the unit circle.

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50

NISSIMOV, E., S. PACHEVA, and S. SOLOMON. "ACTION PRINCIPLE FOR OVERDETERMINED SYSTEMS OF NONLINEAR FIELD EQUATIONS." International Journal of Modern Physics A 04, no. 03 (1989): 737–52. http://dx.doi.org/10.1142/s0217751x89000352.

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We propose a general scheme for constructing an action principle for arbitrary consistent overdetermined systems of nonlinear field equations. The principal tool is the BFV-BRST formalism. There is no need for star-product nor Chern-Simons forms. The main application of this general construction is the derivation of a superspace action in terms of unconstrained superfields for the D = 10N = 1 Super-Yang-Mills theory. The latter contains cubic as well as quartic interactions.

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