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Journal articles on the topic 'Dirac Operators'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 May 2024

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1

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.

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2

Ashrafyan, Yuri, and Tigran Harutyunyan. "Isospectral Dirac operators." Electronic Journal of Qualitative Theory of Differential Equations, no. 4 (2017): 1–9. http://dx.doi.org/10.14232/ejqtde.2017.1.4.

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3

Nolder, Craig A., and John Ryan. "p-Dirac Operators." Advances in Applied Clifford Algebras 19, no. 2 (March 19, 2009): 391–402. http://dx.doi.org/10.1007/s00006-009-0162-7.

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4

Notte-Cuello, E. A. "On the Dirac and Spin-Dirac Operators." Advances in Applied Clifford Algebras 20, no. 3-4 (May 11, 2010): 765–80. http://dx.doi.org/10.1007/s00006-010-0220-1.

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5

Prokhorenkov, Igor, and Ken Richardson. "Perturbations of Dirac operators." Journal of Geometry and Physics 57, no. 1 (December 2006): 297–321. http://dx.doi.org/10.1016/j.geomphys.2006.03.004.

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6

Ryan, John. "Intrinsic Dirac Operators inCn." Advances in Mathematics 118, no. 1 (March 1996): 99–133. http://dx.doi.org/10.1006/aima.1996.0019.

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7

BRIHAYE, Y., and A. NININAHAZWE. "DIRAC OSCILLATORS AND QUASI-EXACTLY SOLVABLE OPERATORS." Modern Physics Letters A 20, no. 25 (August 20, 2005): 1875–85. http://dx.doi.org/10.1142/s0217732305018128.

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The Dirac equation is formulated in the background of three types of physically relevant potentials: scalar, vector and "Dirac-oscillator" potentials. Assuming these potentials to be spherically-symmetric and with generic polynomial forms in the radial variable, we construct the corresponding radial Dirac equation. Cases where this linear spectral equation is exactly solvable or quasi-exactly solvable are worked out in details. When available, relations between the radial Dirac operator and some super-algebra are pointed out.

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8

Baum, Paul F., and Erik van Erp. "K-homology and Fredholm operators I: Dirac operators." Journal of Geometry and Physics 134 (December 2018): 101–18. http://dx.doi.org/10.1016/j.geomphys.2018.08.008.

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9

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.

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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.

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10

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.

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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].

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11

Yang, Chuan-fu, Feng Wang, and Zhen-you Huang. "Ambarzumyan Theorems for Dirac Operators." Acta Mathematicae Applicatae Sinica, English Series 37, no. 2 (April 2021): 287–98. http://dx.doi.org/10.1007/s10255-021-1007-y.

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12

Ono, Kaoru. "Equivariant index of Dirac operators." Tohoku Mathematical Journal 42, no. 3 (1990): 319–32. http://dx.doi.org/10.2748/tmj/1178227613.

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13

Balachandran, A. P., Giorgio Immirzi, Joohan Lee, and Peter Prešnajder. "Dirac operators on coset spaces." Journal of Mathematical Physics 44, no. 10 (2003): 4713. http://dx.doi.org/10.1063/1.1607514.

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14

Albeverio, S., R. Hryniv, and Ya Mykytyuk. "Reconstruction of radial Dirac operators." Journal of Mathematical Physics 48, no. 4 (April 2007): 043501. http://dx.doi.org/10.1063/1.2709847.

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15

Almanasreh, Hasan, and Nils Svanstedt. "G-Convergence of Dirac Operators." Journal of Function Spaces and Applications 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/789875.

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16

Benn, I. M., and J. M. Kress. "First-order Dirac symmetry operators." Classical and Quantum Gravity 21, no. 2 (December 4, 2003): 427–31. http://dx.doi.org/10.1088/0264-9381/21/2/007.

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17

Arrizabalaga, Naiara, Albert Mas, and Luis Vega. "Shell interactions for Dirac operators." Journal de Mathématiques Pures et Appliquées 102, no. 4 (October 2014): 617–39. http://dx.doi.org/10.1016/j.matpur.2013.12.006.

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18

Ginoux, Nicolas. "Dirac operators on Lagrangian submanifolds." Journal of Geometry and Physics 52, no. 4 (December 2004): 480–98. http://dx.doi.org/10.1016/j.geomphys.2004.04.008.

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19

Nguyen, Hans, and Alexander Schenkel. "Dirac operators on noncommutative hypersurfaces." Journal of Geometry and Physics 158 (December 2020): 103917. http://dx.doi.org/10.1016/j.geomphys.2020.103917.

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20

De Schepper, H., D. Eelbode, and T. Raeymaekers. "Twisted Higher Spin Dirac Operators." Complex Analysis and Operator Theory 8, no. 2 (March 24, 2013): 429–47. http://dx.doi.org/10.1007/s11785-013-0295-5.

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21

Fox, Jeffrey, and Peter Haskell. "Comparison of perturbed Dirac operators." Proceedings of the American Mathematical Society 124, no. 5 (1996): 1601–8. http://dx.doi.org/10.1090/s0002-9939-96-03263-7.

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22

Lu, Jianfeng, Alexander B. Watson, and Michael I. Weinstein. "Dirac Operators and Domain Walls." SIAM Journal on Mathematical Analysis 52, no. 2 (January 2020): 1115–45. http://dx.doi.org/10.1137/19m127416x.

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23

Pladdy, Chris, Yoshimi Saitō, and Tomio Umeda. "Radiation condition for Dirac operators." Journal of Mathematics of Kyoto University 37, no. 4 (1997): 567–84. http://dx.doi.org/10.1215/kjm/1250518204.

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24

Brummelhuis, R., and J. Nourrigat. "Scattering amplitude for dirac operators." Communications in Partial Differential Equations 24, no. 1-2 (January 1999): 377–94. http://dx.doi.org/10.1080/03605309908821427.

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25

Martin, Mircea. "Joint seminormality and Dirac operators." Integral Equations and Operator Theory 30, no. 1 (March 1998): 101–21. http://dx.doi.org/10.1007/bf01195879.

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26

Yuan, Hongfen, Zhihai Zhang, and Yuying Qiao. "Polynomial Dirac Operators in Superspace." Advances in Applied Clifford Algebras 25, no. 3 (December 24, 2014): 755–69. http://dx.doi.org/10.1007/s00006-014-0524-7.

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27

Nolder, Craig A., and Guanghong Wang. "Fourier Multipliers and Dirac Operators." Advances in Applied Clifford Algebras 27, no. 2 (January 10, 2017): 1647–57. http://dx.doi.org/10.1007/s00006-016-0752-0.

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28

Esteban, Maria J., and M. Loss. "Self-adjointness for Dirac operators via Hardy-Dirac inequalities." Journal of Mathematical Physics 48, no. 11 (November 2007): 112107. http://dx.doi.org/10.1063/1.2811950.

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29

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.

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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.

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30

Wu, Tong, Jian Wang, and Yong Wang. "Dirac–Witten Operators and the Kastler–Kalau–Walze Type Theorem for Manifolds with Boundary." Journal of Nonlinear Mathematical Physics 29, no. 1 (September 20, 2021): 1–40. http://dx.doi.org/10.1007/s44198-021-00009-6.

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AbstractIn this paper, we obtain two Lichnerowicz type formulas for the Dirac–Witten operators. And we give the proof of Kastler–Kalau–Walze type theorems for the Dirac–Witten operators on 4-dimensional and 6-dimensional compact manifolds with (resp. without) boundary.

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31

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.

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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.

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32

Gwaltney, Ethan. "Dirac operators with operator data of Wigner-von Neumann type." Journal of Differential Equations 391 (May 2024): 370–95. http://dx.doi.org/10.1016/j.jde.2024.02.004.

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33

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.

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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.

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34

Lotfizadeh, M. "Super Ginsparg–Wilson algebra and Dirac operator on the super fuzzy Euclidean hyperboloid EAdSF(2|2)." International Journal of Modern Physics A 35, no. 31 (November 10, 2020): 2050196. http://dx.doi.org/10.1142/s0217751x20501961.

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In this paper, we construct super fuzzy Dirac and chirality operators on the super fuzzy Euclidean hyperboloid [Formula: see text] in-instanton and no-instanton sectors. Using the super pseudo-projectors of the noncompact first Hopf fibration, we construct the Ginsparg–Wilson algebra in instanton and no-instanton sectors. Then, using the generators of this algebra, we construct pseudo super-Dirac and chirality operators in both sectors. We also construct pseudo super-Dirac and chirality operators corresponding to the case in which our theory includes gauge fields. We show that they have correct commutative limit in the limit case when the noncommutative parameter [Formula: see text] tends to infinity.

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35

Simulik, V. M., and I. O. Gordievich. "Symmetries of Relativistic Hydrogen Atom." Ukrainian Journal of Physics 64, no. 12 (December 9, 2019): 1148. http://dx.doi.org/10.15407/ujpe64.12.1148.

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The Dirac equation in the external Coulomb field is proved to possess the symmetry determined by 31 operators, which form the 31-dimensional algebra. Two different fermionic realizations of the SO(1,3) algebra of the Lorentz group are found. Two different bosonic realizations of this algebra are found as well. All generators of the above-mentioned algebras commute with the operator of the Dirac equation in an external Coulomb field and, therefore, determine the algebras of invariance of such Dirac equation. Hence, the spin s = (1, 0) Bose symmetry of the Dirac equation for the free spinor field, proved recently in our papers, is extended here for the Dirac equation interacting with an external Coulomb field. A relativistic hydrogen atom is modeled by such Dirac equation. We are able to prove for the relativistic hydrogen atom both the fermionic and bosonic symmetries known from our papers in the case of a non-interacting spinor field. New symmetry operators are found on the basis of new gamma matrix representations of the Clifford and SO(8) algebras, which are known from our recent papers as well. Hidden symmetries were found both in the canonical Foldy–Wouthuysen and covariant Dirac representations. The found symmetry operators, which are pure matrix ones in the Foldy–Wouthuysen representation, become non-local in the Dirac model.

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36

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.

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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.

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37

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.

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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.

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38

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.

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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.

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39

Müller, David. "Minimax principles, Hardy-Dirac inequalities, and operator cores for two and three dimensional Coulomb-Dirac operators." Documenta Mathematica 21 (2016): 1151–69. http://dx.doi.org/10.4171/dm/554.

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40

Bernstein, Swanhild. "Fundamental solutions for Dirac-type operators." Banach Center Publications 37, no. 1 (1996): 159–72. http://dx.doi.org/10.4064/-37-1-159-172.

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41

Barrera-Figueroa, V., V. S. Rabinovich, and S. A. C. Loredo-Ramírez. "Dirac Operators on Infinite Quantum Graphs." Russian Journal of Mathematical Physics 29, no. 3 (September 2022): 306–20. http://dx.doi.org/10.1134/s1061920822030025.

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42

Kang, Yi Fang, and Zhi Qi Chen. "Dirac Operators on Quadratic Lie Superalgebras." Acta Mathematica Sinica, English Series 37, no. 8 (August 2021): 1229–53. http://dx.doi.org/10.1007/s10114-021-0556-6.

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43

Iantchenko, Alexei, and Evgeny Korotyaev. "Resonances for the radial Dirac operators." Asymptotic Analysis 93, no. 4 (July 17, 2015): 327–70. http://dx.doi.org/10.3233/asy-151298.

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44

BRACKX, F., and H. DE SCHEPPER. "HILBERT-DIRAC OPERATORS IN CLIFFORD ANALYSIS." Chinese Annals of Mathematics 26, no. 01 (January 2005): 1–14. http://dx.doi.org/10.1142/s0252959905000026.

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45

Cerejeiras, P., and J. Cnops. "Hodge—dirac operators for hyperbolic spaces." Complex Variables, Theory and Application: An International Journal 41, no. 3 (May 2000): 267–78. http://dx.doi.org/10.1080/17476930008815254.

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46

Hryniv, Rostyslav O., and Yaroslav V. Mykytyuk. "Eigenvalue asymptotics for Dirac–Bessel operators." Journal of Mathematical Physics 57, no. 6 (June 2016): 063507. http://dx.doi.org/10.1063/1.4953245.

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47

Sitarz, Andrzej. "Twisted Dirac operators over quantum spheres." Journal of Mathematical Physics 49, no. 3 (March 2008): 033509. http://dx.doi.org/10.1063/1.2842067.

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48

Chen, Zhuo, and Mathieu Stiénon. "Dirac generating operators and Manin triples." Journal of the London Mathematical Society 79, no. 2 (February 2, 2009): 399–421. http://dx.doi.org/10.1112/jlms/jdn084.

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49

Harju, Antti J. "Covariant Dirac operators on quantum groups." Journal of Mathematical Physics 52, no. 12 (December 2011): 123509. http://dx.doi.org/10.1063/1.3664284.

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50

OHTA, KAZUTOSHI, and HISAO SUZUKI. "DIRAC OPERATORS ON QUANTUM-TWO SPHERES." Modern Physics Letters A 09, no. 25 (August 20, 1994): 2325–33. http://dx.doi.org/10.1142/s0217732394002197.

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We investigate the spin-1/2 fermions on quantum-two spheres. It is shown that the wave functions of fermions and a Dirac operator on quantum-two spheres can be constructed in a manifestly covariant way under the quantum group SU (2)q. The concept of total angular momentum and chirality can be expressed by using q-analog of Pauli-matrices and appropriate commutation relations.

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