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Books on the topic 'Dirac operator'

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Published: 4 June 2021

Last updated: 8 June 2024

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1

service), SpringerLink (Online, ed. The Dirac spectrum. Berlin: Springer, 2009.

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2

Delanghe, Richard. Clifford algebra and spinor-valued functions: A function theory for the Dirac operator. Dordrecht: Kluwer Academic Publishers, 1992.

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3

The heat kernel Lefschetz fixed point formula for the spin-c dirac operator. Boston: Birkhauser, 1996.

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4

Duistermaat, J. J. The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator. Boston, MA: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8247-7.

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5

Duistermaat, J. J. The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator. Boston, MA: Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4612-5344-0.

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6

service), SpringerLink (Online, ed. The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator. Boston, MA: Springer Science+Business Media, LLC, 2011.

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7

V, Tyutin I., Voronov B. L, and SpringerLink (Online service), eds. Self-adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials. Boston: Birkhäuser Boston, 2012.

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8

1955-, Ryan John, Struppa Daniele Carlo 1955-, and International Society for Analysis, Applications, and Computation. Congress, eds. Dirac operators in analysis. Harlow, Essex, England: Longman, 1998.

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9

S, Sargsi͡a︡n I., ed. Sturm-Liouville and Dirac operators. Dordrecht: Kluwer Academic, 1991.

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10

Berline, Nicole, Ezra Getzler, and Michèle Vergne. Heat Kernels and Dirac Operators. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-58088-8.

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11

Levitan, B. M., and I. S. Sargsjan. Sturm—Liouville and Dirac Operators. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3748-5.

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12

Habermann, Katharina, and Lutz Habermann. Introduction to Symplectic Dirac Operators. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/b138212.

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13

Dirac operators and spectral geometry. Cambridge: Cambridge University Press, 1998.

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14

Thomas, Friedrich. Dirac operators in Riemannian geometry. Providence, R.I: American Mathematical Society, 2000.

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15

Berline, Nicole. Heat kernels and Dirac operators. Berlin: Springer-Verlag, 1992.

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16

Berline, Nicole. Heat kernels and Dirac operators. 2nd ed. Berlin: Springer, 1996.

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17

Booß-Bavnbek, Bernhelm, and Krzysztof P. Wojciechowski. Elliptic Boundary Problems for Dirac Operators. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-0337-7.

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18

Booss, Bernhelm. Elliptic boundary problems for Dirac operators. Boston: Birkhäuser, 1993.

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19

Cnops, Jan. An Introduction to Dirac Operators on Manifolds. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0065-9.

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20

S, Sargsi͡a︡n I., ed. Operatory Shturma-Liuvilli͡a︡ i Diraka. Moskva: "Nauka," Glav. red. fiziko-matematicheskoĭ lit-ry, 1988.

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21

Arai, Asao. Infinite-Dimensional Dirac Operators and Supersymmetric Quantum Fields. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-5678-2.

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22

Gilbert, John E. Clifford algebras and Dirac operators in harmonic analysis. Cambridge [England]: Cambridge University Press, 1991.

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23

Arhancet, Cédric, and Christoph Kriegler. Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99011-4.

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24

1947-, Bourguignon J. P., Center for Advanced Mathematical Sciences., and American University of Beirut, eds. Dirac operators: Yesterday and Today: Proceedings of the summer school and workshop, CAMS-AUB, Lebanon, August 27- September 7, 2001. Somerville, MA: International Press, 2005.

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25

Fushchich, V. I. Symmetries of Maxwell's equations. Dordrecht: D. Reidel, 1987.

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26

Kirk, P. Analytic deformations of the spectrum of a family of Dirac operators on an odd-dimensional manifold with boundary. Providence, RI: American Mathematical Society, 1996.

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27

Fushchich, Vilʹgelʹm Ilʹich. Symmetries of Maxwell's equations. Dordrecht [Netherlands]: D. Reidel, 1987.

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28

Ellwood, D. (David), 1966- editor of compilation, Rodnianski, Igor, 1972- editor of compilation, Staffilani, Gigliola, 1966- editor of compilation, and Wunsch, Jared, editor of compilation, eds. Evolution equations: Clay Mathematics Institute Summer School, evolution equations, Eidgenössische Technische Hochschule, Zürich, Switzerland, June 23-July 18, 2008. Providence, Rhode Island: American Mathematical Society, 2013.

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29

Gilbert, Denis Mareschal, Michael S. C. Thomas, and Iroise Dumontheil. Clifford Algrebras and Dirac Operator. Taylor & Francis Group, 2020.

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30

Horing, Norman J. Morgenstern. Dirac Notation and Transformation Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0001.

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Chapter 1 opens with a brief review of some basic features of quantum mechanics, including the Schrödinger equation, linear and angular momentum and the theory of the hydrogenic atom: It also includes complete orthonormal sets of eigenfunctions, the translation operator, current, spin, equation of continuity, gauge transformation, determinant & permanent multiparticle energy eigenfunctions for noninteracting particles and the Pauli exclusion principle. Attention is then focused on Dirac bra-ket notation and complete sets of commuting observables. In this connection, representations and transformation among representations are discussed in detail for the Schrödinger system state vector and the eigenstates, as well as bra-ket matrix elements of operators. Finally, Schwinger’s interpretation of ket-bra matrix operator structures (Schwinger “Measurement Symbols”) in terms of annihilation and creation of systems in eigenstates is introduced.

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31

Dirac-Operatoren in der Riemannschen Geometrie: Mit einem Ausblick auf die Seiberg-Witten-Theorie. Wiesbaden: Vieweg+Teubner Verlag, 1997.

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32

Dirac Operators in Representation Theory. Springer London, Limited, 2006.

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33

Huang, Jing-Song, and Pavle Pandzic. Dirac Operators in Representation Theory. Springer, 2008.

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34

Marino, Marcos. Quantum chromodynamics. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.32.

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Abstract:

This article focuses on chiral random matrix theories with the global symmetries of quantum chromodynamics (QCD). In particular, it explains how random matrix theory (RMT) can be applied to the spectra of the Dirac operator both at zero chemical potential, when the Dirac operator is Hermitian, and at non-zero chemical potential, when the Dirac operator is non-Hermitian. Before discussing the spectra of these Dirac operators at non-zero chemical potential, the article considers spontaneous symmetry breaking in RMT and the QCD partition function. It then examines the global symmetries of QCD, taking into account the Dirac operator for a finite chiral basis, as well as the global symmetry breaking pattern and the Goldstone manifold in chiral random matrix theory (chRMT). It also describes the generating function for the Dirac spectrum and applications of chRMT to QCD to gauge degrees of freedom.

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35

Duistermaat, J. J. Heat Kernel Lefschetz Fixed Point Formula for the Spin-C Dirac Operator. Birkhauser Verlag, 1996.

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36

Dirac Operators in Representation Theory (Mathematics: Theory & Applications). Birkhäuser Boston, 2006.

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37

Delanghe, R. Clifford Algebra and Spinor-Valued Functions: A Function Theory For The Dirac Operator. V Soucek R Delanghe F Sommen, 2012.

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38

The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator. Birkhäuser, 2011.

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39

Delanghe, R., F. Sommen, and V. Soucek. Clifford Algebra and Spinor-Valued Functions: A Function Theory for the Dirac Operator. Springer, 2012.

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40

Duistermaat, J. J. The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator. Birkhäuser, 2011.

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41

The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator. Birkhäuser, 2011.

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42

Nonlinear Dirac Equation: Spectral Stability of Solitary Waves. American Mathematical Society, 2020.

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43

Dirac Operators in Representation Theory. Boston, MA: Birkhäuser Boston, 2007. http://dx.doi.org/10.1007/978-0-8176-4493-2.

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44

Dirac Operators Yesterday and Today. International Press of Boston, Incorporated, 2010.

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45

Sargsjan, I. S., and Levitan. Sturm--Liouville and Dirac Operators. Springer, 2012.

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46

Levitan and I. S. Sargsjan. Sturm―Liouville and Dirac Operators. Springer, 2012.

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47

Bourguignon, Jean-Pierre. Dirac Operators: Yesterday and Today. International Press, 2005.

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48

Esposito, Giampiero. Dirac Operators and Spectral Geometry. Cambridge University Press, 2010.

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49

Esposito, Giampiero. Dirac Operators and Spectral Geometry. Cambridge University Press, 2011.

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50

Cnops, Jan. Introduction to Dirac Operators on Manifolds. Birkhauser Verlag, 2012.

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