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1

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

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2

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

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3

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

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4

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

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5

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

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6

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

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7

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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8

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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9

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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10

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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11

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

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12

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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13

Friedrich, Thomas. Dirac-Operatoren in der Riemannschen Geometrie. Wiesbaden: Vieweg+Teubner Verlag, 1997. http://dx.doi.org/10.1007/978-3-322-80302-3.

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14

Planit, Michael. Operators Are Standing By! New York: McGraw-Hill, 2007.

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15

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

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16

Spectral geometry: Direct and inverse problems. Berlin: Springer-Verlag, 1986.

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17

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

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18

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

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19

Thomas, Friedrich. Dirac-Operatoren in der Riemannschen Geometrie: Mit einem Ausblick auf die Seiberg-Witten-Theorie. Braunschweig: Vieweg, 1997.

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20

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

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21

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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22

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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23

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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24

Operators are standing by: Surefire direct response marketing that keeps customers calling! New York: McGraw-Hill Professional, 2007.

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25

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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26

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

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27

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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28

United States. Congress. Senate. Committee on Governmental Affairs. Permanent Subcommittee on Investigations. The hidden operators of deceptive mailings: Hearing before the Permanent Subcommittee on Investigations of the Committee on Governmental Affairs, United States Senate, One Hundred Sixth Congress, first session, July 20, 1999. Washington: U.S. G.P.O., 1999.

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29

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

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30

United States. Congress. House. Committee on Resources. Subcommittee on Water and Power. H.R. 1071, to direct the Secretary of Energy to make incentive payments to the owners or operators of qualified desalination facilities; and oversight on "reducing power and other costs of the desalination process": Legislative and oversight hearing before the Subcommittee on Water and Power of the Committee on Resources, U.S. House of Representatives, One Hundred Ninth Congress, first session, Tuesday, May 24, 2005. Washington: U.S. G.P.O., 2005.

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31

Power, United States Congress House Committee on Resources Subcommittee on Water and. H.R. 1071, to direct the Secretary of Energy to make incentive payments to the owners or operators of qualified desalination facilities; and oversight on "reducing power and other costs of the desalination process": Legislative and oversight hearing before the Subcommittee on Water and Power of the Committee on Resources, U.S. House of Representatives, One Hundred Ninth Congress, first session, Tuesday, May 24, 2005. Washington: U.S. G.P.O., 2005.

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32

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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33

Desalination Water Supply Shortage Prevention Act and Water Supply Technology Program Act: Hearing before the Committee on Energy and Natural Resources, United States Senate, One Hundred Ninth Congress, first session, on S. 1016, a bill to direct the Secretary of Energy to make incentive payments to the owners or operators of qualified desalination facilities to partially offset the cost of electrical energy required to operate the facilities, and for other purposes; S. 1860, a bill to amend the Energy Policy Act of 2005 to improve energy production and reduce energy demand through improved use of reclaimed waters, and for other purposes, October 20, 2005. Washington: U.S. G.P.O., 2006.

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34

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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35

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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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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36

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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37

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

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38

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

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39

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

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40

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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41

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

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42

Booß-Bavnbek, Bernhelm. Elliptic Boundary Problems for Dirac Operators. Springer, 2012.

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43

An Introduction to Dirac Operators on Manifolds. Birkhäuser Boston, 2002.

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44

Cnops, Jan. An Introduction to Dirac Operators on Manifolds. Springer, 2012.

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45

Planit, Michael. Operators Are Standing By. McGraw-Hill, 2007.

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46

Planit, Michael. Operators Are Standing By. McGraw-Hill, 2007.

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47

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

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48

Heat Kernels and Dirac Operators (Grundlehren Text Editions). Springer, 2004.

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49

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

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50

Murray, M., and J. Gilbert. Clifford Algebras and Dirac Operators in Harmonic Analysis. Cambridge University Press, 2008.

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