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Journal articles on the topic 'Gauge invariant variational approach'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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1

SOKOŁOWSKI, LESZEK M. "GENERAL RELATIVITY, GRAVITATIONAL ENERGY AND SPIN–TWO FIELD." International Journal of Geometric Methods in Modern Physics 04, no. 01 (February 2007): 147–69. http://dx.doi.org/10.1142/s0219887807001904.

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In my lectures I will deal with three seemingly unrelated problems: i) to what extent is general relativity exceptional among metric gravity theories? ii) is it possible to define gravitational energy density applying field–theory approach to gravity? and iii) can a consistent theory of a gravitationally interacting spin–two field be developed at all? The connecting link to them is the concept of a fundamental classical spin–2 field. A linear spin–2 field introduced as a small perturbation of a Ricci–flat spacetime metric, is gauge invariant while its energy–momentum is gauge dependent. Furthermore, when coupled to gravity, the field reveals insurmountable inconsistencies in the resulting equations of motion. After discussing the inconsistencies of any coupling of the linear spin–2 field to gravity, I exhibit the origin of the fact that a gauge invariant field has the variational metric stress tensor which is gauge dependent. I give a general theorem explaining under what conditions a symmetry of a field Lagrangian becomes also the symmetry of the variational stress tensor. It is a conclusion of the theorem that any attempt to define gravitational energy density in the framework of a field theory of gravity must fail. Finally I make a very brief introduction to basic concepts of how a certain kind of a necessarily nonlinear spin–2 field arises in a natural way from vacuum nonlinear metric gravity theories (Lagrangian being any scalar function of Ricci tensor). This specific spin–2 field consistently interacts gravitationally and the theory of the field is promising.

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2

Tiwari, S. C. "Axion electrodynamics in the duality perspective." Modern Physics Letters A 30, no. 40 (December 28, 2015): 1550204. http://dx.doi.org/10.1142/s0217732315502041.

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Axion electrodynamics is deduced from the local duality invariant electrodynamics (LDIE) with a new perspective on both formalism and the physical interpretation. First, the delicate issue of duality rotation symmetry in the Maxwell action is critically reviewed and the generalized Maxwell field equations invariant under local duality rotation are derived. In the alternative approach, a generalization is made to Sudbery’s pseudo-vector action such that it is local duality invariant. Variational principle is used to derive the Euler–Lagrange equations of motion. The gauge potential for local duality rotation, termed duroton, under the assumption that it is a gradient of the axion field leads to the dual symmetric axion electrodynamics. The absence of the magnetic monopole in Maxwell equations motivates to impose a natural condition to deduce the standard axion electrodynamics. The present derivation offers the possibility for new physical interpretation of the axions and the monopoles.

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3

ISLAM, M. M., and S. J. PUGLIA. "ANOMALOUS CHIRAL ACTION FROM THE PATH INTEGRAL." International Journal of Modern Physics A 13, no. 04 (February 10, 1998): 523–51. http://dx.doi.org/10.1142/s0217751x98000226.

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By generalizing the Fujikawa approach, we show in the path integral formalism: (1) how the infinitesimal variation of the fermion measure can be integrated to obtain the full anomalous chiral action; (2) how the action derived in this way can be identified as the Chern–Simons term in five dimensions, if the anomaly is consistent; (3) how the regularization can be carried out, so as to lead to the consistent anomaly and not to the covariant anomaly. We consider a massless left-handed fermion interacting with a non-Abelian gauge field. The gauge field also interacts with a set of Goldstone bosons, so that a gauge-invariant configuration of the gauge field exists. We use Schwinger's "proper time" representation of the Green's function and the guage-invariant point-splitting technique, and find that the consistency requirement and the point-splitting technique allow both an anomalous and a nonanomalous action. In the end, the nature of the vacuum determines whether we have an anomalous theory or a nonanomalous theory.

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4

Lipatov, Lev N. "Euler-Lagrange equations for high energy effective actions in QCD and in gravity." International Journal of Modern Physics: Conference Series 39 (January 2015): 1560082. http://dx.doi.org/10.1142/s2010194515600824.

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We review the theory of the high energy scattering in QCD and gravity based on effective actions local in rapidities of usual and reggeized particles. The Euler-Lagrange equations are constructed with a variational approach for these actions and by using the invariance under the gauge and general coordinate transformations.

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5

Lipatov, L. N. "Euler-Lagrange equations for the Gribov reggeon calculus in QCD and in gravity." International Journal of Modern Physics A 31, no. 28n29 (October 19, 2016): 1645011. http://dx.doi.org/10.1142/s0217751x16450111.

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The theory of the high energy scattering in QCD and gravity is based on the reggeization of gluons and gravitons, respectively. We discuss the corresponding effective actions for reggeized particle interactions. The Euler-Lagrange equations in these theories are constructed with a variational approach for the effective actions and by using their invariance under the gauge and general coordinate transformations.

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6

Cremaschini, Claudio, and Massimo Tessarotto. "Manifest Covariant Hamiltonian Theory of General Relativity." Applied Physics Research 8, no. 2 (March 16, 2016): 60. http://dx.doi.org/10.5539/apr.v8n2p60.

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The problem of formulating a manifest covariant Hamiltonian theory of General Relativity in the presence of source ﬁelds is addressed, by extending the so-called “DeDonder-Weyl” formalism to the treatment of classical ﬁelds in curved space-time. The theory is based on a synchronous variational principle for the Einstein equation, formulated in terms of superabundant variables. The technique permits one to determine the continuum covariant Hamiltonian structure associated with the Einstein equation. The corresponding continuum Poisson bracket representation is also determined. The theory relies on ﬁrst-principles, in the sense that the conclusions are reached in the framework of a non-perturbative covariant approach, which allows one to preserve both the 4-scalar nature of Lagrangian and Hamiltonian densities as well as the gauge invariance property of the theory.

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7

POPOVA, A. D., and A. N. PETROV. "NONLINEAR QUANTUM MECHANICS WITH NONCLASSICAL GRAVITATIONAL SELF-INTERACTION III: RELATED TOPICS." International Journal of Modern Physics A 08, no. 16 (June 30, 1993): 2709–34. http://dx.doi.org/10.1142/s0217751x93001089.

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Some problems are considered in the framework of general quantum mechanics with gravitational self-interaction constructed earlier. A number of them were analyzed for the stationary situation. Here, the problem of gauge invariance generated by translations which do not violate the 3 + 1 splitting is studied. The notions of position and momentum operators are extended to the general case. The uncertainty relations are obtained for the uncertainty of the Ricci tensor and for uncertainties of the position and momentum of a particle. The correspondence between the stationary and nonstationary cases is examined at the level of variational principles. At least, the one-particle and two-particle problems in the Newtonian–Schrödingerian limit are considered; the latter problem is compared with the standard two-particle quantum problem to demonstrate the advantage of our approach.

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8

Castrillón, López, and Masqué Muñoz. "Hamiltonian structure of gauge-invariant variational problems." Advances in Theoretical and Mathematical Physics 16, no. 1 (2012): 39–63. http://dx.doi.org/10.4310/atmp.2012.v16.n1.a2.

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9

Kopeikin, Sergei M., Juan Ramirez, Bahram Mashhoon, and Mikhail V. Sazhin. "Cosmological perturbations: a new gauge-invariant approach." Physics Letters A 292, no. 3 (December 2001): 173–80. http://dx.doi.org/10.1016/s0375-9601(01)00777-0.

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10

FERRARIS, MARCO, MAURO FRANCAVIGLIA, MARCELLA PALESE, and EKKEHART WINTERROTH. "GAUGE-NATURAL NOETHER CURRENTS AND CONNECTION FIELDS." International Journal of Geometric Methods in Modern Physics 08, no. 01 (February 2011): 177–85. http://dx.doi.org/10.1142/s0219887811005075.

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We study geometric aspects concerned with symmetries and conserved quantities in gauge-natural invariant variational problems and investigate implications of the existence of a reductive split structure associated with canonical Lagrangian conserved quantities on gauge-natural bundles. In particular, we characterize the existence of covariant conserved quantities in terms of principal Cartan connections on gauge-natural prolongations.

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11

Mańka, R. "The variational approach to the pure gauge theory." Annals of Physics 171, no. 1 (October 1986): 1–16. http://dx.doi.org/10.1016/s0003-4916(86)80020-3.

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12

Khan, Hafsa, and Pervez Hoodbhoy. "Systematic gauge-invariant approach to heavy quarkonium decays." Physical Review D 53, no. 5 (March 1, 1996): 2534–40. http://dx.doi.org/10.1103/physrevd.53.2534.

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13

Bonanno, A., and V. Romano. "Flux-limited gauge-invariant approach to cosmological perturbations." Physical Review D 49, no. 12 (June 15, 1994): 6450–59. http://dx.doi.org/10.1103/physrevd.49.6450.

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14

Woszczyna, Andrzej. "Gauge-invariant cosmic structures—A dynamic systems approach." Physical Review D 45, no. 6 (March 15, 1992): 1982–88. http://dx.doi.org/10.1103/physrevd.45.1982.

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15

Swiecicki, Sylvia D., and J. E. Sipe. "Gauge-invariant Green function dynamics: A unified approach." Annals of Physics 338 (November 2013): 260–77. http://dx.doi.org/10.1016/j.aop.2013.09.014.

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16

BRUNO, DANILO, GIANVITTORIO LURIA, and ENRICO PAGANI. "ON THE GAUGE STRUCTURE OF THE CALCULUS OF VARIATIONS WITH CONSTRAINTS." International Journal of Geometric Methods in Modern Physics 08, no. 08 (December 2011): 1723–46. http://dx.doi.org/10.1142/s0219887811005890.

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A gauge-invariant formulation of constrained variational calculus, based on the introduction of the bundle of affine scalars over the configuration manifold, is presented. In the resulting setup, the "Lagrangian" ℒ is replaced by a section of a suitable principal fiber bundle over the velocity space. A geometric rephrasement of Pontryagin's maximum principle, showing the equivalence between a constrained variational problem in the state space and a canonically associated free one in a higher affine bundle, is proved.

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17

AKIHO, NOBUYUKI, FUMIO HIAI, and DÉNES PETZ. "EQUILIBRIUM STATES AND THEIR ENTROPY DENSITIES IN GAUGE-INVARIANT C*-SYSTEMS." Reviews in Mathematical Physics 17, no. 04 (May 2005): 365–89. http://dx.doi.org/10.1142/s0129055x05002352.

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A gauge-invariant C*-system is obtained as the fixed point subalgebra of the infinite tensor product of full matrix algebras under the tensor product unitary action of a compact group. In this paper, thermodynamics is studied in such systems and the chemical potential theory developed by Araki, Haag, Kastler and Takesaki is used. As a generalization of quantum spin system, the equivalence of the KMS condition, the Gibbs condition and the variational principle is shown for translation-invariant states. The entropy density of extremal equilibrium states is also investigated in relation to macroscopic uniformity.

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18

DERIGLAZOV, A. A. "VARIATIONAL PROBLEM FOR THE FRENKEL AND THE BARGMANN–MICHEL–TELEGDI (BMT) EQUATIONS." Modern Physics Letters A 28, no. 01 (January 8, 2013): 1250234. http://dx.doi.org/10.1142/s0217732312502343.

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We propose Lagrangian formulation for the particle with value of spin fixed within the classical theory. The Lagrangian is invariant under non-Abelian group of local symmetries. On this reason, all the initial spin variables turn out to be unobservable quantities. As the gauge-invariant variables for description of spin we can take either the Frenkel tensor or the Bargmann–Michel–Telegdi (BMT) vector. Fixation of spin within the classical theory implies O(ℏ)-corrections to the corresponding equations of motion.

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19

Kerler, Werner, and Lothar Schülke. "Higher-order action-variational approach to Lattice gauge theory." Physics Letters B 201, no. 1 (January 1988): 123–27. http://dx.doi.org/10.1016/0370-2693(88)90092-5.

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20

Tanimura, Nobuko. "Action-variational approach to SU(3) pure gauge theory." Physics Letters B 221, no. 1 (April 1989): 55–59. http://dx.doi.org/10.1016/0370-2693(89)90191-3.

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21

Kumar, R., and A. Shukla. "Christ–Lee Model: Augmented Supervariable Approach." Advances in High Energy Physics 2018 (October 11, 2018): 1–12. http://dx.doi.org/10.1155/2018/7381387.

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We derive the complete set of off-shell nilpotent and absolutely anticommuting (anti-)BRST as well as (anti-)co-BRST symmetry transformations for the gauge-invariant Christ–Lee model by exploiting the celebrated (dual-)horizontality conditions together with the gauge-invariant and (anti-)co-BRST invariant restrictions within the framework of geometrical “augmented” supervariable approach to BRST formalism. We show the (anti-)BRST and (anti-)co-BRST invariances of the Lagrangian in the context of supervariable approach. We also provide the geometrical origin and capture the key properties associated with the (anti-)BRST and (anti-)co-BRST symmetry transformations (and corresponding conserved charges) in terms of the supervariables and Grassmannian translational generators.

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22

PANZA, P., and R. SOLDATI. "MASSIVE AXIAL GAUGE IN THE EXACT RENORMALIZATION GROUP APPROACH." International Journal of Modern Physics A 16, no. 11 (April 30, 2001): 2101–4. http://dx.doi.org/10.1142/s0217751x01004773.

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The Exact Renormalization Group (ERG) approach to massive gauge theories in the axial gauge is studied and the smoothness of the massless limit is analysed for a formally gauge invariant quantity such as the Euclidean Wilson loop.

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23

Paquet, Daniel. "Gauge-invariant tight-binding approach to magnetotunneling in superlattices." Physical Review B 39, no. 11 (April 15, 1989): 7776–87. http://dx.doi.org/10.1103/physrevb.39.7776.

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24

Naus, H. W. L. "Construction of gauge invariant effective nucleonic theories: Functional approach." Nuclear Physics A 628, no. 2 (January 1998): 275–95. http://dx.doi.org/10.1016/s0375-9474(97)00628-3.

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25

Zapata, José A. "A combinatorial approach to diffeomorphism invariant quantum gauge theories." Journal of Mathematical Physics 38, no. 11 (November 1997): 5663–81. http://dx.doi.org/10.1063/1.532159.

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26

Ellis, G. F. R., and M. Bruni. "Covariant and gauge-invariant approach to cosmological density fluctuations." Physical Review D 40, no. 6 (September 15, 1989): 1804–18. http://dx.doi.org/10.1103/physrevd.40.1804.

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27

Kim, Seung-Kook, Yong-Wan Kim, and Young-Jai Park. "Two different gauge-invariant models in the Lagrangian approach." Journal of Physics A: Mathematical and General 31, no. 43 (October 30, 1998): 8677–87. http://dx.doi.org/10.1088/0305-4470/31/43/011.

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28

De, Asit K. "Non-perturbative chiral gauge theories: an overview of a gauge non-invariant approach." Indian Journal of Physics 95, no. 8 (June 24, 2021): 1639–49. http://dx.doi.org/10.1007/s12648-021-02156-4.

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29

Adak, Muzaffer. "Gauge approach to the symmetric teleparallel gravity." International Journal of Geometric Methods in Modern Physics 15, no. 12 (December 2018): 1850198. http://dx.doi.org/10.1142/s0219887818501980.

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We discuss a gauge invariant gravity model in a non-Riemannian geometry in which the curvature and the torsion both are zero, the nonmetricity is nonzero. We also argue that only a metric ansatz is enough to start finding solutions to the field equations. As an application, we obtain explicitly a conformally flat solution.

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30

BUCHBINDER, I. L., V. D. PERSHIN, and G. B. TODER. "ON A GAUGE INVARIANT QUANTUM FORMULATION FOR NON-GAUGE CLASSICAL THEORY." Modern Physics Letters A 11, no. 19 (June 21, 1996): 1589–95. http://dx.doi.org/10.1142/s0217732396001582.

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We propose a method of constructing a gauge invariant canonical formulation for non-gauge classical theory which depends on a set of parameters. Requirement of closure for algebra of operators generating quantum gauge transformations leads to restrictions on parameters of the theory. This approach is then applied for illustration to bosonic string theory coupled to background tachyonic field. It is shown that within the proposed canonical formulation the known mass-shell condition for tachyon is produced.

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31

Oh, Junghyun, and Gyuho Eoh. "Variational Bayesian Approach to Condition-Invariant Feature Extraction for Visual Place Recognition." Applied Sciences 11, no. 19 (September 26, 2021): 8976. http://dx.doi.org/10.3390/app11198976.

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As mobile robots perform long-term operations in large-scale environments, coping with perceptual changes becomes an important issue recently. This paper introduces a stochastic variational inference and learning architecture that can extract condition-invariant features for visual place recognition in a changing environment. Under the assumption that a latent representation of the variational autoencoder can be divided into condition-invariant and condition-sensitive features, a new structure of the variation autoencoder is proposed and a variational lower bound is derived to train the model. After training the model, condition-invariant features are extracted from test images to calculate the similarity matrix, and the places can be recognized even in severe environmental changes. Experiments were conducted to verify the proposed method, and the experimental results showed that our assumption was reasonable and effective in recognizing places in changing environments.

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32

ARNONE, S., YU A. KUBYSHIN, T. R. MORRIS, and J. F. TIGHE. "A GAUGE INVARIANT REGULATOR FOR THE ERG." International Journal of Modern Physics A 16, no. 11 (April 30, 2001): 1989–2001. http://dx.doi.org/10.1142/s0217751x0100461x.

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A gauge invariant regularisation for dealing with pure Yang-Mills theories within the exact renormalization group approach is proposed. It is based on the regularisation via covariant higher derivatives and includes auxiliary Pauli-Villars fields which amounts to a spontaneously broken SU(N|N) super-gauge theory. We demonstrate perturbatively that the extended theory is ultra-violet finite in four dimensions and argue that it has a sensible limit when the regularization cutoff is removed.

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33

GUENDELMAN, E. I. "ZERO ENERGY GAUGE FIELDS AND THE PHASES OF A GAUGE THEORY." International Journal of Modern Physics A 05, no. 14 (July 20, 1990): 2783–98. http://dx.doi.org/10.1142/s0217751x9000129x.

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A new approach to the definition of the phases of a Poincare invariant gauge theory is developed. It is based on the role of gauge transformations that change the asymptotic value of the gauge fields from zero to a constant. In the context of theories without Higgs fields, this symmetry can be spontaneously broken when the gauge fields are massless particles, explicitly broken when the gauge fields develop a mass. Finally, the vacuum can be invariant under this transformation, this last case can be achieved when the theory has a violent infrared behavior, which in some theories can be connected to a confinement mechanism.

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34

WAKAMATSU, MASASHI. "ARE THERE INFINITELY MANY DECOMPOSITIONS OF THE NUCLEON SPIN?" International Journal of Modern Physics: Conference Series 25 (January 2014): 1460031. http://dx.doi.org/10.1142/s2010194514600313.

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We argue against the rapidly spreading idea of gauge-invariant-extension (GIE) approach in the nucleon spin decomposition problem, which implies the existence of infinitely many gauge-invariant decomposition of the nucleon spin.

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35

Bringuier, E. "Gauge-invariant approach to thermodiffusion in a liquid binary mixture." Physica A: Statistical Mechanics and its Applications 390, no. 11 (June 2011): 1861–75. http://dx.doi.org/10.1016/j.physa.2011.01.027.

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36

Potter, William J., and Sirichai Chongchitnan. "A gauge-invariant approach to interactions in the dark sector." Journal of Cosmology and Astroparticle Physics 2011, no. 09 (September 1, 2011): 005. http://dx.doi.org/10.1088/1475-7516/2011/09/005.

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37

Sisakyan, A. N., N. B. Skachkov, I. L. Solovtsov, and O. Yu Shevchenko. "Gauge-invariant approach and infrared behavior of the spinor propagator." Theoretical and Mathematical Physics 78, no. 2 (February 1989): 185–91. http://dx.doi.org/10.1007/bf01018684.

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38

Fournel, C., J. François, S. Lazzarini, and T. Masson. "Gauge invariant composite fields out of connections, with examples." International Journal of Geometric Methods in Modern Physics 11, no. 03 (March 2014): 1450016. http://dx.doi.org/10.1142/s0219887814500169.

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In this paper, we put forward a systematic and unifying approach to construct gauge invariant composite fields out of connections. It relies on the existence in the theory of a group-valued field with a prescribed gauge transformation. As an illustration, we detail some examples. Two of them are based on known results: the first one provides a reinterpretation of the symmetry breaking mechanism of the electroweak part of the Standard Model of particle physics; the second one is an application to Einstein's theory of gravity described as a gauge theory in terms of Cartan connections. The last example depicts a new situation: starting with a gauge field theory on Atiyah Lie algebroids, the gauge invariant composite fields describe massive vector fields. Some mathematical and physical discussions illustrate and highlight the relevance and the generality of this approach.

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39

Mańka, R., and J. Sladkowski. "The variational approach to the extended Glashow–Weinberg–Salam model." Canadian Journal of Physics 66, no. 4 (April 1, 1988): 369–71. http://dx.doi.org/10.1139/p88-059.

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40

HAHN, ATLE. "AN ANALYTIC APPROACH TO TURAEV'S SHADOW INVARIANT." Journal of Knot Theory and Its Ramifications 17, no. 11 (November 2008): 1327–85. http://dx.doi.org/10.1142/s021821650800666x.

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In the present paper, we extend the "torus gauge fixing" approach by Blau and Thompson, which was developed in [10] for the study of Chern–Simons models with base manifolds M of the form M = Σ × S1, in a suitable way. We arrive at a heuristic path integral formula for the Wilson loop observables associated to general links in M. We then show that the right-hand side of this formula can be evaluated explicitly in a non-perturbative way and that this evaluation naturally leads to the face models in terms of which Turaev's shadow invariant is defined.

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41

SATHIAPALAN, B. "LOOP VARIABLES AND GAUGE-INVARIANT INTERACTIONS — II." International Journal of Modern Physics A 16, no. 10 (April 20, 2001): 1679–701. http://dx.doi.org/10.1142/s0217751x01002762.

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We continue the discussion of our previous paper on writing down gauge-invariant interacting equations for a bosonic string using the loop variable approach. In the earlier paper the equations were written down in one higher dimension where the fields are massless. In this paper we describe a procedure for dimensional reduction that gives interacting equations for fields with the same spectrum as in bosonic string theory. We also argue that the on-shell scattering amplitudes implied by these equations for the physical modes are the same as for the bosonic string. We check this explicitly for some of the simpler equations. The gauge transformation of space–time fields induced by gauge transformations of the loop variables are discussed in some detail. The unintegrated (i.e. before the Koba–Nielsen integration), regularized version of the equations, are gauge invariant off-shell (i.e. off the free mass shell).

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42

SATHIAPALAN, B. "LOOP VARIABLES AND GAUGE-INVARIANT INTERACTIONS — I." International Journal of Modern Physics A 15, no. 30 (December 10, 2000): 4761–95. http://dx.doi.org/10.1142/s0217751x00001907.

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We describe a method of writing down interacting equations for all the modes of the bosonic open string. It is a generalization of the loop variable approach that was used earlier for the free, and lowest order interacting cases. The generalization involves, as before, the introduction of a parameter to label the different strings involved in an interaction. The interacting string has thus becomes a "band" of finite width. The interaction equations expressed in terms of loop variables, has a simple invariance that is exact even off shell. A consistent definition of space–time fields requires the fields to be functions of all the infinite number of gauge coordinates (in addition to space–time coordinates). The theory is formulated in one higher dimension, where the modes appear massless. The dimensional reduction that is needed to make contact with string theory (which has been discussed earlier for the free case) is not discussed here.

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43

ESPOSITO, GIAMPIERO, and COSIMO STORNAIOLO. "FROM PEIERLS BRACKETS TO A GENERALIZED MOYAL BRACKET FOR TYPE-I GAUGE THEORIES." International Journal of Geometric Methods in Modern Physics 04, no. 03 (May 2007): 349–60. http://dx.doi.org/10.1142/s0219887807002107.

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In the space-of-histories approach to gauge fields and their quantization, the Maxwell, Yang–Mills and gravitational field are well known to share the property of being type-I theories, i.e. Lie brackets of the vector fields which leave the action functional invariant are linear combinations of such vector fields, with coefficients of linear combination given by structure constants. The corresponding gauge-field operator in the functional integral for the in-out amplitude is an invertible second-order differential operator. For such an operator, we consider advanced and retarded Green functions giving rise to a Peierls bracket among group-invariant functionals. Our Peierls bracket is a Poisson bracket on the space of all group-invariant functionals in two cases only: either the gauge-fixing is arbitrary but the gauge fields lie on the dynamical sub-space; or the gauge-fixing is a linear functional of gauge fields, which are generic points of the space of histories. In both cases, the resulting Peierls bracket is proved to be gauge-invariant by exploiting the manifestly covariant formalism. Moreover, on quantization, a gauge-invariant Moyal bracket is defined that reduces to iħ times the Peierls bracket to lowest order in ħ.

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44

Jiang, Jianlin, Shun Zhang, Su Zhang, and Jie Wen. "A variational inequality approach for constrained multifacility Weber problem under gauge." Journal of Industrial & Management Optimization 14, no. 3 (2018): 1085–104. http://dx.doi.org/10.3934/jimo.2017091.

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45

Kerler, Werner, and Thomas Metz. "Higher-order action-variational approach to SU(3) lattice gauge theory." Physics Letters B 229, no. 3 (October 1989): 264–68. http://dx.doi.org/10.1016/0370-2693(89)91169-6.

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46

Ibarra, Alejandro, Eduard Massó, and Javier Redondo. "Systematic approach to gauge-invariant relations between lepton flavor violating processes." Nuclear Physics B 715, no. 1-2 (May 2005): 523–35. http://dx.doi.org/10.1016/j.nuclphysb.2005.03.017.

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47

Fried, H. M., T. Grandou, and Y. M. Sheu. "A new approach to analytic, non-perturbative and gauge-invariant QCD." Annals of Physics 327, no. 11 (November 2012): 2666–90. http://dx.doi.org/10.1016/j.aop.2012.07.008.

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48

Fried, H. M., P. H. Tsang, Y. Gabellini, T. Grandou, and Y. M. Sheu. "An exact, finite, gauge-invariant, non-perturbative approach to QCD renormalization." Annals of Physics 359 (August 2015): 1–19. http://dx.doi.org/10.1016/j.aop.2015.03.024.

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49

Rybkin, G. N. "Batalin-Fradkin-Vilkovisky approach for gauge invariant systems with closed algebra." Physics Letters B 275, no. 3-4 (January 1992): 341–44. http://dx.doi.org/10.1016/0370-2693(92)91599-5.

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50

FENG, SHIPING, TIANXING MA, and JIHONG QIN. "GAUGE INVARIANT DRESSED HOLON AND SPINON IN DOPED CUPRATES." Modern Physics Letters B 17, no. 09 (April 20, 2003): 361–73. http://dx.doi.org/10.1142/s0217984903005251.

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Abstract:

We develop a partial charge-spin separation fermion-spin theory implemented by the gauge invariant dressed holon and spinon. In this novel approach, the physical electron is decoupled as the gauge invariant dressed holon and spinon, with the dressed holon behaviors like a spinful fermion, and represents the charge degree of freedom together with the phase part of the spin degree of freedom, while the dressed spinon is a hard-core boson, and represents the amplitude part of the spin degree of freedom, then the electron single occupancy local constraint is satisfied. Within this approach, the charge transport and spin response of the underdoped cuprates is studied. It is shown that the charge transport is mainly governed by the scattering from the dressed holons due to the dressed spinon fluctuation, while the scattering from the dressed spinons due to the dressed holon fluctuation dominates the spin response.

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