Log in

Relevant bibliographies by topics / Dirac operator / Journal articles

Journal articles on the topic 'Dirac operator'

To see the other types of publications on this topic, follow the link: Dirac operator.

Author: Grafiati

Published: 4 June 2021

Last updated: 8 June 2024

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Dirac operator.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Patra, Rashmirekha, and Nihar Ranjan Satapathy. "Novel finite difference approach to discretize the symplectic dirac operator." Annals of Mathematics and Computer Science 18 (October 1, 2023): 90–103. http://dx.doi.org/10.56947/amcs.v18.211.

Full text

Abstract:

Symplectic Dirac operator is an intertwining differential operator. Discretising symplectic Dirac operator gives a new direction to study the quantum space. The construction of discrete symplectic Dirac operator requires the theory of discrete symplectic Clifford analysis or the concept of discrete symplectic connections, which are not explained in literature. In this work, a discretization approach for symplectic Dirac operator is suggested by considering the forward and backward basis vectors on symplectic Clifford algebra. The suggested discrete symplectic Dirac operator is Ds=Ds++Ds- where the Ds+ and Ds- are the forward and backward discrete symplectic Dirac operators, respectively. The new discrete symplectic Dirac operator gives the factorization of discrete Laplacian on symplectic spaces. Further, we establish commutation relations involving forward and backward discrete symplectic Dirac operators in the representation theory.

APA, Harvard, Vancouver, ISO, and other styles

2

AVRAMIDI, IVAN G. "DIRAC OPERATOR IN MATRIX GEOMETRY." International Journal of Geometric Methods in Modern Physics 02, no. 02 (April 2005): 227–64. http://dx.doi.org/10.1142/s0219887805000636.

Full text

Abstract:

We review the construction of the Dirac operator and its properties in Riemannian geometry, and show how the asymptotic expansion of the trace of the heat kernel determines the spectral invariants of the Dirac operator and its index. We also point out that the Einstein–Hilbert functional can be obtained as a linear combination of the first two spectral invariants of the Dirac operator. Next, we report on our previous attempts to generalize the notion of the Dirac operator to the case of Matrix Geometry, where, instead of a Riemannian metric there is a matrix valued self-adjoint symmetric two-tensor that plays a role of a "non-commutative" metric. We construct invariant first-order and second-order self-adjoint elliptic partial differential operators, which can be called "non-commutative" Dirac operators and non-commutative Laplace operators. We construct the corresponding heat kernel for the non-commutative Laplace type operator and compute its first two spectral invariants. A linear combination of these two spectral invariants gives a functional that can be considered as a non-commutative generalization of the Einstein–Hilbert action.

APA, Harvard, Vancouver, ISO, and other styles

3

Yuan, Hongfen, Guohong Shi, and Xiushen Hu. "Boundary Value Problems for the Perturbed Dirac Equation." Axioms 13, no. 4 (April 4, 2024): 238. http://dx.doi.org/10.3390/axioms13040238.

Full text

Abstract:

The perturbed Dirac operators yield a factorization for the well-known Helmholtz equation. In this paper, using the fundamental solution for the perturbed Dirac operator, we define Cauchy-type integral operators (singular integral operators with a Cauchy kernel). With the help of these operators, we investigate generalized Riemann and Dirichlet problems for the perturbed Dirac equation which is a higher-dimensional generalization of a Vekua-type equation. Furthermore, applying the generalized Cauchy-type integral operator F˜λ, we construct the Mann iterative sequence and prove that the iterative sequence strongly converges to the fixed point of operator F˜λ.

APA, Harvard, Vancouver, ISO, and other styles

4

MATSUTANI, SHIGEKI. "DIRAC OPERATOR ON A CONFORMAL SURFACE IMMERSED IN ℝ4: A WAY TO FURTHER GENERALIZED WEIERSTRASS EQUATION." Reviews in Mathematical Physics 12, no. 03 (March 2000): 431–44. http://dx.doi.org/10.1142/s0129055x00000149.

Full text

Abstract:

In the previous report (J. Phys.A30 (1997) 4019–4029), I showed that the Dirac operator defined over a conformal surface immersed in ℝ3 by means of confinement procedure is identified with the differential operator of the generalized Weierstrass equation and the Lax operator of the modified Novikov–Veselov (MNV) equation. In this article, using the same procedure, I determine the Dirac operator defined over a conformal surface immersed in ℝ4, which is for a Dirac field confined in the surface. Then it is reduced to the Lax operators of the nonlinear Schrödinger and the MNV equations by taking appropriate limits. It means that the Dirac operator is related to the further generalized Weierstrass equation for a surface in ℝ4.

APA, Harvard, Vancouver, ISO, and other styles

5

Cojuhari, Petru, and Aurelian Gheondea. "Embeddings, Operator Ranges, and Dirac Operators." Complex Analysis and Operator Theory 5, no. 3 (April 13, 2010): 941–53. http://dx.doi.org/10.1007/s11785-010-0066-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

DABROWSKI, LUDWIK, ANDRZEJ SITARZ, and ALESSANDRO ZUCCA. "DIRAC OPERATORS ON NONCOMMUTATIVE PRINCIPAL CIRCLE BUNDLES." International Journal of Geometric Methods in Modern Physics 11, no. 01 (December 16, 2013): 1450012. http://dx.doi.org/10.1142/s0219887814500121.

Full text

Abstract:

We study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle. Examples of low-dimensional noncommutative tori are analyzed in more detail and all connections found that are compatible with an admissible Dirac operator. Conversely, a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection is exhibited. These examples are extended to the theta-deformed principal U(1)-bundle [Formula: see text].

APA, Harvard, Vancouver, ISO, and other styles

7

KHACHIDZE, TAMARI T., and ANZOR A. KHELASHVILI. "AN "ACCIDENTAL" SYMMETRY OPERATOR FOR THE DIRAC EQUATION IN THE COULOMB POTENTIAL." Modern Physics Letters A 20, no. 30 (September 28, 2005): 2277–81. http://dx.doi.org/10.1142/s0217732305018505.

Full text

Abstract:

On the basis of the generalization of the theorem about K-odd operators (K is the Dirac's operator), certain linear combination is constructed, which appears to commute with the Dirac Hamiltonian for Coulomb field. This operator coincides with the Johnson and Lippmann operator and is closely connected to the familiar Laplace–Runge–Lenz vector. Our approach guarantees not only derivation of Johnson–Lippmann operator, but simultaneously commutativity with the Dirac Hamiltonian.

APA, Harvard, Vancouver, ISO, and other styles

8

Henheik, Joscha, and Roderich Tumulka. "Interior-boundary conditions for the Dirac equation at point sources in three dimensions." Journal of Mathematical Physics 63, no. 12 (December 1, 2022): 122302. http://dx.doi.org/10.1063/5.0104675.

Full text

Abstract:

A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians with particle creation is based on interior-boundary conditions (IBCs). The approach works well in the non-relativistic case, i.e., for the Laplacian operator. Here, we study how the approach can be applied to Dirac operators. While this has successfully been done already in one space dimension, and more generally for codimension-1 boundaries, the situation of point sources in three dimensions corresponds to a codimension-3 boundary. One would expect that, for such a boundary, Dirac operators do not allow for boundary conditions because they are known not to allow for point interactions in 3D, which also correspond to a boundary condition. Indeed, we confirm this expectation here by proving that there is no self-adjoint operator on a (truncated) Fock space that would correspond to a Dirac operator with an IBC at configurations with a particle at the origin. However, we also present a positive result showing that there are self-adjoint operators with an IBC (on the boundary consisting of configurations with a particle at the origin) that are away from those configurations, given by a Dirac operator plus a sufficiently strong Coulomb potential.

APA, Harvard, Vancouver, ISO, and other styles

9

TANIŞLI, MURAT, MUSTAFA EMRE KANSU, and SÜLEYMAN DEMİR. "SUPERSYMMETRIC QUANTUM MECHANICS AND EUCLIDEAN–DIRAC OPERATOR WITH COMPLEXIFIED QUATERNIONS." Modern Physics Letters A 28, no. 08 (March 12, 2013): 1350026. http://dx.doi.org/10.1142/s0217732313500260.

Full text

Abstract:

We propose an alternative formulation of the supersymmetric quantum mechanics and Euclidean Dirac and Dirac–Yang–Mills (DYM) operators in terms of complexified quaternions. 4×4 matrix representations of the complexified quaternions are used to express the Euclidean–Dirac operator and Yang–Mills gauge field.

APA, Harvard, Vancouver, ISO, and other styles

10

Aastrup, Johannes, and Jesper Møller Grimstrup. "The quantum holonomy-diffeomorphism algebra and quantum gravity." International Journal of Modern Physics A 31, no. 10 (April 6, 2016): 1650048. http://dx.doi.org/10.1142/s0217751x16500482.

Full text

Abstract:

We introduce the quantum holonomy-diffeomorphism ∗-algebra, which is generated by holonomy-diffeomorphisms on a three-dimensional manifold and translations on a space of SU(2)-connections. We show that this algebra encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Furthermore, we show that semiclassical states exist on the holonomy-diffeomorphism part of the algebra but that these states cannot be extended to the full algebra. Via a Dirac-type operator we derive a certain class of unbounded operators that act in the GNS construction of the semiclassical states. These unbounded operators are the type of operators, which we have previously shown to entail the spatial three-dimensional Dirac operator and Dirac–Hamiltonian in a semiclassical limit. Finally, we show that the structure of the Hamilton constraint emerges from a Yang–Mills-type operator over the space of SU(2)-connections.

APA, Harvard, Vancouver, ISO, and other styles

11

Benameur, Moulay-Tahar, James L. Heitsch, and Charlotte Wahl. "An interesting example for spectral invariants." Journal of K-Theory 13, no. 2 (April 2014): 305–11. http://dx.doi.org/10.1017/is014002020jkt255.

Full text

Abstract:

AbstractIn [HL99], the heat operator of a Bismut superconnection for a family of generalized Dirac operators is defined along the leaves of a foliation with Hausdorff groupoid. The Novikov-Shubin invariants of the Dirac operators were assumed greater than three times the codimension of the foliation. It was then shown that the associated heat operator converges to the Chern character of the index bundle of the operator. In [BH08], this result was improved by reducing the requirement on the Novikov-Shubin invariants to one half of the codimension. In this paper, we construct examples which show that this is the best possible result.

APA, Harvard, Vancouver, ISO, and other styles

12

Schmidt, Karl Michael. "Dense point spectrum for the one-dimensional Dirac operator with an electrostatic potential." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 126, no. 5 (1996): 1087–96. http://dx.doi.org/10.1017/s0308210500023271.

Full text

Abstract:

For the one-dimensional Dirac operator, examples of electrostatic potentials with decay behaviour arbitrarily close to Coulomb decay are constructed for which the operator has a prescribed set of eigenvalues dense in the whole or part of its essential spectrum. A simple proof that the essential spectrum of one-dimensional Dirac operators with electrostatic potentials is never empty is given in the appendix.

APA, Harvard, Vancouver, ISO, and other styles

13

ARAI, ASAO. "HEISENBERG OPERATORS, INVARIANT DOMAINS AND HEISENBERG EQUATIONS OF MOTION." Reviews in Mathematical Physics 19, no. 10 (November 2007): 1045–69. http://dx.doi.org/10.1142/s0129055x07003206.

Full text

Abstract:

An abstract operator theory is developed on operators of the form AH(t) := eitHAe-itH, t ∈ ℝ, with H a self-adjoint operator and A a linear operator on a Hilbert space (in the context of quantum mechanics, AH(t) is called the Heisenberg operator of A with respect to H). The following aspects are discussed: (i) integral equations for AH(t) for a general class of A; (ii) a sufficient condition for D(A), the domain of A, to be left invariant by e-itH for all t ∈ ℝ; (iii) a mathematically rigorous formulation of the Heisenberg equation of motion in quantum mechanics and the uniqueness of its solutions; (iv) invariant domains in the case where H is an abstract version of Schrödinger and Dirac operators; (v) applications to Schrödinger operators with matrix-valued potentials and Dirac operators.

APA, Harvard, Vancouver, ISO, and other styles

14

CHALUB, FABIO A. C. C. "On Huygens' principle for Dirac operators associated to electromagnetic fields." Anais da Academia Brasileira de Ciências 73, no. 4 (December 2001): 483–93. http://dx.doi.org/10.1590/s0001-37652001000400002.

Full text

Abstract:

We study the behavior of massless Dirac particles, i.e., solutions of the Dirac equation with m = 0 in the presence of an electromagnetic field. Our main result (Theorem 1) is that for purely real or imaginary fields any Huygens type (in Hadamard's sense) Dirac operators is equivalent to the free Dirac operator, equivalence given by changes of variables and multiplication (right and left) by nonzero functions.

APA, Harvard, Vancouver, ISO, and other styles

15

GINOUX, NICOLAS, and BERTRAND MOREL. "ON EIGENVALUE ESTIMATES FOR THE SUBMANIFOLD DIRAC OPERATOR." International Journal of Mathematics 13, no. 05 (July 2002): 533–48. http://dx.doi.org/10.1142/s0129167x0200140x.

Full text

Abstract:

We give lower bounds for the eigenvalues of the submanifold Dirac operator in terms of intrinsic and extrinsic curvature expressions. We also show that the limiting cases give rise to a class of spinor fields generalizing that of Killing spinors. We conclude by translating these results in terms of intrinsic twisted Dirac operators.

APA, Harvard, Vancouver, ISO, and other styles

16

Lotfizadeh, M., and Ebrahim Nouri Asl. "Pseudo generalization of Ginsparg–Wilson algebra on the fuzzy EAdS2 including gauge fields." International Journal of Geometric Methods in Modern Physics 17, no. 03 (February 14, 2020): 2050046. http://dx.doi.org/10.1142/s0219887820500462.

Full text

Abstract:

Using the gauged pseudo-Hermitian fuzzy Ginsparg–Wilson algebra, pseudo fuzzy Dirac and chirality operators on the fuzzy [Formula: see text] have been studied. Also, the spectrum of the gauged pseudo fuzzy Dirac operator in the instanton sector has been studied.

APA, Harvard, Vancouver, ISO, and other styles

17

Arai, Asao, and Dayantsolmon Dagva. "A Class of -Dimensional Dirac Operators with a Variable Mass." ISRN Mathematical Analysis 2013 (July 1, 2013): 1–13. http://dx.doi.org/10.1155/2013/913413.

Full text

Abstract:

A class of d-dimensional Dirac operators with a variable mass is introduced (), which includes, as a special case, the 3-dimensional Dirac operator describing the chiral quark soliton model in nuclear physics, and some aspects of it are investigated.

APA, Harvard, Vancouver, ISO, and other styles

18

Wang, Yong. "A Kastler-Kalau-Walze Type Theorem and the Spectral Action for Perturbations of Dirac Operators on Manifolds with Boundary." Abstract and Applied Analysis 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/619120.

Full text

Abstract:

We prove a Kastler-Kalau-Walze type theorem for perturbations of Dirac operators on compact manifolds with or without boundary. As a corollary, we give two kinds of operator-theoretic explanations of the gravitational action on boundary. We also compute the spectral action for Dirac operators with two-form perturbations on 4-dimensional compact manifolds.

APA, Harvard, Vancouver, ISO, and other styles

19

Monakhov, Vadim. "The Dirac Sea, T and C Symmetry Breaking, and the Spinor Vacuum of the Universe." Universe 7, no. 5 (May 1, 2021): 124. http://dx.doi.org/10.3390/universe7050124.

Full text

Abstract:

We have developed a quantum field theory of spinors based on the algebra of canonical anticommutation relations (CAR algebra) of Grassmann densities in the momentum space. We have proven the existence of two spinor vacua. Operators C and T transform the normal vacuum into an alternative one, which leads to the breaking of the C and T symmetries. The CPT is the real structure operator; it preserves the normal vacuum. We have proven that, in the theory of the Dirac Sea, the formula for the charge conjugation operator must contain an additional generalized Dirac conjugation operator.

APA, Harvard, Vancouver, ISO, and other styles

20

FAN, HONGYI, and YUE FAN. "WEYL ORDERING FOR ENTANGLED STATE REPRESENTATION." International Journal of Modern Physics A 17, no. 05 (February 20, 2002): 701–8. http://dx.doi.org/10.1142/s0217751x02003257.

Full text

Abstract:

We derive a new Weyl ordering operator formula which recasts given operators into Weyl ordering. In so doing, the Weyl ordering formulation of the entangled state representation is obtained, which turns out to be the Weyl ordered Dirac δ-operator functions. The Weyl ordering of the Wigner operator and squeezing operator in entangled state representation are also deduced.

APA, Harvard, Vancouver, ISO, and other styles

21

BRACKX, F., D. EELBODE, T. RAEYMAEKERS, and L. VAN DE VOORDE. "TRIPLE MONOGENIC FUNCTIONS AND HIGHER SPIN DIRAC OPERATORS." International Journal of Mathematics 22, no. 06 (June 2011): 759–74. http://dx.doi.org/10.1142/s0129167x11007021.

Full text

Abstract:

In the Clifford analysis context a specific type of solution for the higher spin Dirac operators [Formula: see text] is studied; these higher spin Dirac operators can be seen as generalizations of the classical Rarita–Schwinger operator. To that end subspaces of the space of triple monogenic polynomials are introduced and their algebraic structure is investigated. Also a dimensional analysis is carried out.

APA, Harvard, Vancouver, ISO, and other styles

22

Ferrando, Juan Carlos. "A Dirac Delta Operator." Mathematics and Statistics 9, no. 2 (March 2021): 179–87. http://dx.doi.org/10.13189/ms.2021.090213.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

van der Schaft, Arjan, and Bernhard Maschke. "Differential operator Dirac structures." IFAC-PapersOnLine 54, no. 19 (2021): 198–203. http://dx.doi.org/10.1016/j.ifacol.2021.11.078.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Fakhri, Hossein, and Ali Imaanpur. "Dirac operator on fuzzyAdS2." Journal of High Energy Physics 2003, no. 03 (March 3, 2003): 003. http://dx.doi.org/10.1088/1126-6708/2003/03/003.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Bieske, Thomas, and John Ryan. "The infinite Dirac operator." Journal of Physics: Conference Series 254 (November 1, 2010): 012003. http://dx.doi.org/10.1088/1742-6596/254/1/012003.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

CAMPOS, RAFAEL G., J. L. LÓPEZ-LÓPEZ, and R. VERA. "LATTICE CALCULATIONS ON THE SPECTRUM OF DIRAC AND DIRAC–KÄHLER OPERATORS." International Journal of Modern Physics A 23, no. 07 (March 20, 2008): 1029–38. http://dx.doi.org/10.1142/s0217751x08038470.

Full text

Abstract:

We use a lattice formulation to study the spectra of the Dirac and the Dirac–Kähler operators on the 2-sphere. This lattice formulation uses differentiation matrices which yield exact values for the derivatives of polynomials, preserving the Leibniz rule in subspaces of polynomials of low degree and therefore, this formulation can be used to study the fermion–boson symmetry on the lattice. In this context, we find that the free Dirac and Dirac–Kähler operators on the 2-sphere exhibit fermionic as well as bosonic-like eigensolutions for which the corresponding eigenvalues and the number of states are computed. In the Dirac case these solutions appear in doublets, except for the bosonic mode with zero eigenvalue, indicating the possible existence of a supersymmetry of the square of the Dirac operator.

APA, Harvard, Vancouver, ISO, and other styles

27

Kath, Ines, and Oliver Ungermann. "Spectra of Sub-Dirac Operators on Certain Nilmanifolds." MATHEMATICA SCANDINAVICA 117, no. 1 (September 28, 2015): 64. http://dx.doi.org/10.7146/math.scand.a-22237.

Full text

Abstract:

We study sub-Dirac operators associated to left-invariant bracket-generating sub-Riemannian structures on compact quotients of nilpotent semi-direct products $G=\mathsf{R}^n\rtimes_A\mathsf{R}$. We prove that these operators admit an $L^2$-basis of eigenfunctions. Explicit examples of this type show that the spectrum of these operators can be non-discrete and that eigenvalues may have infinite multiplicity. In this case the sub-Dirac operator is neither Fredholm nor hypoelliptic.

APA, Harvard, Vancouver, ISO, and other styles

28

Jin, Ming, Guangbin Ren, and Irene Sabadini. "Slice Dirac operator over octonions." Israel Journal of Mathematics 240, no. 1 (September 23, 2020): 315–44. http://dx.doi.org/10.1007/s11856-020-2067-z.

Full text

Abstract:

AbstractThe slice Dirac operator over octonions is a slice counterpart of the Dirac operator over quaternions. It involves a new theory of stem functions, which is the extension from the commutative O(1) case to the non-commutative O(3) case. For functions in the kernel of the slice Dirac operator over octonions, we establish the representation formula, the Cauchy integral formula (and, more in general, the Cauchy-Pompeiu formula), and the Taylor as well as the Laurent series expansion formulas.

APA, Harvard, Vancouver, ISO, and other styles

29

Fatibene, Lorenzo, Raymond G. McLenaghan, and Giovanni Rastelli. "Symmetry operators and separation of variables for Dirac's equation on two-dimensional spin manifolds with external fields." International Journal of Geometric Methods in Modern Physics 12, no. 01 (December 28, 2014): 1550012. http://dx.doi.org/10.1142/s0219887815500127.

Full text

Abstract:

The second-order symmetry operators that commute with the Dirac operator with external vector, scalar and pseudo-scalar potentials are computed on a general two-dimensional spin manifold. It is shown that the operator is defined in terms of Killing vectors, valence two Killing tensors and scalar fields defined on the background manifold. The commuting operator that arises from a non-trivial Killing tensor is determined with respect to the associated system of Liouville coordinates and compared to the second-order operator that obtained from the unique separation scheme associated with such operators. It is shown by the study of several examples that the operators arising from these two approaches coincide.

APA, Harvard, Vancouver, ISO, and other styles

30

Inskeep, Warren H. "On Electromagnetic Spinors and Electron Theory." Zeitschrift für Naturforschung A 44, no. 4 (April 1, 1989): 327–28. http://dx.doi.org/10.1515/zna-1989-0414.

Full text

Abstract:

Abstract The relationship between the Dirac theory and electromagnetic spinors is extended to the case of finite mass. Certain products of the electromagnetic fields give rise to the Dirac differential operator upon the usual subsitutions for the energy and momentum. By placing mass in the proper place for the wave mechanical approach to quantum theory, the algebra of the fields, interpreted as quantum operators, may be deduced.

APA, Harvard, Vancouver, ISO, and other styles

31

HARIKUMAR, E. ""SCHWINGER MODEL" ON THE FUZZY SPHERE." Modern Physics Letters A 25, no. 37 (December 7, 2010): 3151–67. http://dx.doi.org/10.1142/s0217732310034079.

Full text

Abstract:

In this paper, we construct a model of spinor fields interacting with specific gauge fields on the fuzzy sphere and analyze the chiral symmetry of this "Schwinger model". In constructing the theory of gauge fields interacting with spinors on the fuzzy sphere, we take the approach that the Dirac operator Dq on the q-deformed fuzzy sphere [Formula: see text] is the gauged Dirac operator on the fuzzy sphere. This introduces interaction between spinors and specific one-parameter family of gauge fields. We also show how to express the field strength for this gauge field in terms of the Dirac operators Dq and D alone. Using the path integral method, we have calculated the 2n-point functions of this model and show that, in general, they do not vanish, reflecting the chiral non-invariance of the partition function.

APA, Harvard, Vancouver, ISO, and other styles

32

Petitjean, Michel. "Chirality of Dirac Spinors Revisited." Symmetry 12, no. 4 (April 14, 2020): 616. http://dx.doi.org/10.3390/sym12040616.

Full text

Abstract:

We emphasize the differences between the chirality concept applied to relativistic fermions and the ususal chirality concept in Euclidean spaces. We introduce the gamma groups and we use them to classify as direct or indirect the symmetry operators encountered in the context of Dirac algebra. Then we show how a recent general mathematical definition of chirality unifies the chirality concepts and resolve conflicting conclusions about symmetry operators, and particularly about the so-called chirality operator. The proofs are based on group theory rather than on Clifford algebras. The results are independent on the representations of Dirac gamma matrices, and stand for higher dimensional ones.

APA, Harvard, Vancouver, ISO, and other styles

33

Korotyaev, Evgeny, and Dmitrii Mokeev. "Periodic Dirac operator with dislocation." Journal of Differential Equations 296 (September 2021): 369–411. http://dx.doi.org/10.1016/j.jde.2021.06.006.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

Hogreve, H. "The overcritical Dirac–Coulomb operator." Journal of Physics A: Mathematical and Theoretical 46, no. 2 (December 10, 2012): 025301. http://dx.doi.org/10.1088/1751-8113/46/2/025301.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Nikolov, Petko A., and Gergana R. Ruseva. "Dimensional reduction of Dirac operator." Journal of Mathematical Physics 47, no. 7 (July 2006): 073503. http://dx.doi.org/10.1063/1.2217811.

Full text

APA, Harvard, Vancouver, ISO, and other styles

36

Akemann, G., and P. H. Damgaard. "Distributions of Dirac operator eigenvalues." Physics Letters B 583, no. 1-2 (March 2004): 199–206. http://dx.doi.org/10.1016/j.physletb.2003.12.024.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Damgaard, P. H. "The microscopic dirac operator spectrum." Nuclear Physics B - Proceedings Supplements 106-107 (March 2002): 29–37. http://dx.doi.org/10.1016/s0920-5632(01)01640-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Nishida, Gou, and Bernhard Maschke. "Stokes-Dirac operator for Laplacian." IFAC-PapersOnLine 52, no. 16 (2019): 430–35. http://dx.doi.org/10.1016/j.ifacol.2019.11.818.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Dowker, J. S. "Spherical Dirac GJMS operator determinants." Journal of Physics A: Mathematical and Theoretical 48, no. 2 (December 9, 2014): 025401. http://dx.doi.org/10.1088/1751-8113/48/2/025401.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Hijazi, Oussama, Sebastián Montiel, and Xiao Zhang. "Dirac Operator on Embedded Hypersurfaces." Mathematical Research Letters 8, no. 2 (2001): 195–208. http://dx.doi.org/10.4310/mrl.2001.v8.n2.a8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Kastler, Daniel. "The dirac operator and gravitation." Communications in Mathematical Physics 166, no. 3 (January 1995): 633–43. http://dx.doi.org/10.1007/bf02099890.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Cornean, H. D., M. Moscolari, and K. S. Sørensen. "Bulk–edge correspondence for unbounded Dirac–Landau operators." Journal of Mathematical Physics 64, no. 2 (February 1, 2023): 021902. http://dx.doi.org/10.1063/5.0119022.

Full text

Abstract:

We consider two-dimensional unbounded magnetic Dirac operators, either defined on the whole plane or with infinite mass boundary conditions on a half-plane. Our main results use techniques from elliptic PDEs and integral operators, while their topological consequences are presented as corollaries of some more general identities involving magnetic derivatives of local traces of fast decaying functions of the bulk and edge operators. One of these corollaries leads to the so-called Středa formula: if the bulk operator has an isolated compact spectral island, then the integrated density of states of the corresponding bulk spectral projection varies linearly with the magnetic field as long as the gaps between the spectral island and the rest of the spectrum are not closed, and the slope of this variation is given by the Chern character of the projection. The same bulk Chern character is related to the number of edge states that appear in the gaps of the bulk operator.

APA, Harvard, Vancouver, ISO, and other styles

43

Ciurla, D., L. Hadasz, and T. E. Williams. "A Superspace Dirac Operator in NCG and the “Factorization” of the Ordinary Dirac Operator." Acta Physica Polonica B 52, no. 12 (2021): 1449. http://dx.doi.org/10.5506/aphyspolb.52.1449.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Nagase, Masayoshi. "Twistor spaces and the adiabatic limits of Dirac operators." Nagoya Mathematical Journal 164 (December 2001): 53–73. http://dx.doi.org/10.1017/s0027763000008035.

Full text

Abstract:

We show that a (Spinq-style) twistor space admits a canonical Spin structure. The adiabatic limits of η-invariants of the associated Dirac operator and of an intrinsically twisted Dirac operator are then investigated.

APA, Harvard, Vancouver, ISO, and other styles

45

LOYA, PAUL, SERGIU MOROIANU, and RAPHAËL PONGE. "ON THE SINGULARITIES OF THE ZETA AND ETA FUNCTIONS OF AN ELLIPTIC OPERATOR." International Journal of Mathematics 23, no. 06 (May 6, 2012): 1250020. http://dx.doi.org/10.1142/s0129167x11007616.

Full text

Abstract:

Let P be a self-adjoint elliptic operator of order m > 0 acting on the sections of a Hermitian vector bundle over a compact Riemannian manifold of dimension n. General arguments show that its zeta and eta functions may have poles only at points of the form [Formula: see text], where k ranges over all nonzero integers ≤ n. In this paper, we construct elementary and explicit examples of perturbations of P which make the zeta and eta functions become singular at all points at which they are allowed to have singularities. We proceed within three classes of operators: Dirac-type operators, self-adjoint first-order differential operators and self-adjoint elliptic pseudodifferential operators. As consequences, we obtain genericity results for the singularities of the zeta and eta functions in those settings. In particular, in the setting of Dirac-type operators we obtain a purely analytical proof of a well-known result of Branson–Gilkey [Residues of the eta function for an operator of Dirac type, J. Funct. Anal. 108(1) (1992) 47–87], which was obtained by invoking Riemannian invariant theory. As it turns out, the results of this paper contradict Theorem 6.3 of [R. Ponge, Spectral asymmetry, zeta functions and the noncommutative residue, Int. J. Math. 17 (2006) 1065–1090]. Corrections to that statement are given in this paper.

APA, Harvard, Vancouver, ISO, and other styles

46

Caban, Paweł, Jakub Rembieliński, and Marta Włodarczyk. "Covariant Abstract Description for a Dirac Particle." Open Systems & Information Dynamics 19, no. 04 (December 2012): 1250027. http://dx.doi.org/10.1142/s1230161212500278.

Full text

Abstract:

We give a direct link between covariant description of Dirac particles in the abstract framework of unitary representation of the Poincaré group and description with the help of the Dirac equation. In this context we discuss the spin operator for a relativistic Dirac particle. We show also that the spin operator used in quantum field theory for spin s = 1/2 corresponds to the Foldy-Wouthuysen mean-spin operator. We hope that this formalism will be useful in the theory of relativistic quantum information.

APA, Harvard, Vancouver, ISO, and other styles

47

Branson, Thomas, and Oussama Hijazi. "Vanishing Theorems and Eigenvalue Estimates in Riemannian Spin Geometry." International Journal of Mathematics 08, no. 07 (November 1997): 921–34. http://dx.doi.org/10.1142/s0129167x97000433.

Full text

Abstract:

We use the representation theory of the structure group Spin (n), together with the theory of conformally covariant differential operators, to generalize results estimating eigenvalues of the Dirac operator to other tensor-spinor bundles, and to get vanishing theorems for the kernels of first-order differential operators.

APA, Harvard, Vancouver, ISO, and other styles

48

IVANOV, E. A., and A. V. SMILGA. "DIRAC OPERATOR ON COMPLEX MANIFOLDS AND SUPERSYMMETRIC QUANTUM MECHANICS." International Journal of Modern Physics A 27, no. 25 (October 10, 2012): 1230024. http://dx.doi.org/10.1142/s0217751x12300244.

Full text

Abstract:

We explore a simple [Formula: see text] supersymmetric quantum mechanics (SQM) model describing the motion over complex manifolds in external gauge fields. The nilpotent supercharge Q of the model can be interpreted as a (twisted) exterior holomorphic derivative, such that the model realizes the twisted Dolbeault complex. The sum [Formula: see text] can be interpreted as the Dirac operator: the standard Dirac operator if the manifold is Kähler and the Dirac operator involving certain particular extra torsions for a generic complex manifold. Focusing on the Kähler case, we give new simple physical proofs of the two mathematical facts: (i) the equivalence of the twisted Dirac and twisted Dolbeault complexes and (ii) the Atiyah–Singer theorem.

APA, Harvard, Vancouver, ISO, and other styles

49

KAWARABAYASHI, TOHRU, YASUHIRO HATSUGAI, TAKAHIRO MORIMOTO, and HIDEO AOKI. "GENERALIZATION OF CHIRAL SYMMETRY FOR TILTED DIRAC CONES." International Journal of Modern Physics: Conference Series 11 (January 2012): 145–50. http://dx.doi.org/10.1142/s2010194512006046.

Full text

Abstract:

The notion of chiral symmetry for the conventional Dirac cone is generalized to include the tilted Dirac cones, where the generalized chiral operator turns out to be non-hermitian. It is shown that the generalized chiral symmetry generically protects the zero modes (n = 0 Landau level) of the Dirac cone even when tilted. The present generalized symmetry is equivalent to the condition that the Dirac Hamiltonian is elliptic as a differential operator, which provides an explicit relevance to the index theorem.

APA, Harvard, Vancouver, ISO, and other styles

50

HOFF DA SILVA, J. M., and ROLDÃO DA ROCHA. "FROM DIRAC ACTION TO ELKO ACTION." International Journal of Modern Physics A 24, no. 16n17 (July 10, 2009): 3227–42. http://dx.doi.org/10.1142/s0217751x09044218.

Full text

Abstract:

A fundamental action, representing a mass dimension-transmuting operator between Dirac and ELKO spinor fields, is performed on the Dirac Lagrangian, in order to lead it into the ELKO Lagrangian. Such a dynamical transformation can be seen as a natural extension of the Standard Model that incorporates dark matter fields. The action of the mass dimension-transmuting operator on a Dirac spinor field, that defines and introduces such a mapping, is shown to be a composition of the Dirac operator and the nonunitary transformation that maps Dirac spinor fields into ELKO spinor fields, defined in J. Math. Phys.48, 123517 (2007). This paper gives allowance for ELKO, as a candidate to describe dark matter, to be incorporated in the Standard Model. It is intended to present for the first time, up to our knowledge, the dynamical character of a mapping between Dirac and ELKO spinor fields, transmuting the mass dimension of spin one-half fermionic fields from 3/2 to 1 and from 1 to 3/2.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!