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001450505 020__ $$a9811956782$$q(electronic bk.)
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001450505 0247_ $$a10.1007/978-981-19-5678-2$$2doi
001450505 035__ $$aSP(OCoLC)1348376010
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001450505 050_4 $$aQC174.45
001450505 08204 $$a530.14/3$$223/eng/20221031
001450505 1001_ $$aArai, Asao,$$d1954-$$eauthor.
001450505 24510 $$aInfinite-dimensional Dirac operators and supersymmetric quantum fields :$$ban introduction to analysis on Boson-Fermion Fock spaces /$$cAsao Arai.
001450505 264_1 $$aSingapore :$$bSpringer,$$c[2022]
001450505 264_4 $$c©2022
001450505 300__ $$a1 online resource (xiii, 117 pages) :$$billustrations.
001450505 336__ $$atext$$btxt$$2rdacontent
001450505 337__ $$acomputer$$bc$$2rdamedia
001450505 338__ $$aonline resource$$bcr$$2rdacarrier
001450505 4901_ $$aSpringerBriefs in mathematical physics ;$$vvolume 46
001450505 504__ $$aIncludes bibliographical references and index.
001450505 5050_ $$aIntro -- Preface -- Contents -- Symbols -- Numbers -- Operational Symbols -- Other Symbols -- 1 Abstract Supersymmetric Quantum Mechanics -- 1.1 Definition and Basic Properties -- 1.2 Reflection Symmetry of the Spectrum of a Self-adjoint Supercharge -- 1.3 Orthogonal Decomposition of State Vectors -- 1.4 Operator Matrix Representations -- 1.5 Construction of SQM -- 1.5.1 Method I -- 1.5.2 Method II -- 1.6 Spectral Supersymmetry -- 1.7 Ground States -- 1.8 Spontaneous Supersymmetry Breaking and an Index Formula -- 2 Elements of the Theory of Fock Spaces -- 2.1 Full Fock Space
001450505 5058_ $$a2.2 Boson Fock Space -- 2.3 Fermion Fock Space -- 2.4 Second Quantization Operators on the Full Fock Space -- 2.5 Boson Second Quantization Operators -- 2.6 Fermion Second Quantization Operators -- 2.7 Infinite Determinants -- 2.8 Boson Creation and Annihilation Operators -- 2.9 Segal Field Operator -- 2.10 Isomorphisms Among Boson Fock Spaces -- 2.11 Fermion Creation and Annihilation Operators -- 2.12 Fermion Quadratic Operators -- 3 Q-space Representation of Boson Fock Space -- 3.1 Gaussian Random Process -- 3.2 Natural Isomorphism of Boson Fock Spaces -- 3.3 Gradient Operator
001450505 5058_ $$a3.4 More General Natural Isomorphisms of Boson Fock Spaces -- 4 Boson-Fermion Fock Spaces and Abstract Supersymmetric Quantum Field Models -- 4.1 Boson-Fermion Fock Space -- 4.2 Q-Space Representation of Boson-Fermion Fock Space -- 4.3 Exterior Differential Operators -- 4.3.1 Definitions and Basic Properties -- 4.3.2 A Cochain Complex -- 4.4 Operators in the Q-space Representation -- 4.5 Hilbert Complex -- 4.5.1 Definitions and Basic Facts -- 4.5.2 Laplace-Beltrami Operators of Finite Order and de Rham-Hodge-Kodaira Decompositions
001450505 5058_ $$a4.5.3 The Dirac and the Laplace-Beltrami Operators Associated With a Hilbert Complex -- 4.5.4 Supersymmetric Structure -- 4.6 Hilbert Complexes Associated With Boson-Fermion Fock Space -- 4.7 Laplace-Beltrami Operators on Boson-Fermion Fock Space -- 4.8 Dirac Operators on Boson-Fermion Fock Space -- 4.9 Strong Anti-Commutativity of Dirac Operators -- 4.10 Perturbations of Dirac Operator QS -- 4.10.1 Witten Deformation -- 4.10.2 More General Perturbations -- 4.11 Explicit Form of Supersymmetric Hamiltonian HS(F) -- 4.12 Path Integral Representation of the Index of QS,+(F)
001450505 5058_ $$a4.12.1 Path Integral Representations of Pure Imaginary Time Correlation Functions of Bose Fields -- 4.12.2 Index Formula -- 5 Models in Supersymmetric Quantum Field Theory -- 5.1 Preliminaries -- 5.1.1 Momentum Operator of a Quantum Particle in Tell -- 5.1.2 The Free Quantum Klein-Gordon Field on Mell -- 5.1.3 The Majorana Field on Mell -- 5.2 The N=1 Wess-Zumino Model on Mell -- 5.2.1 The Free Case -- 5.2.2 The Interacting Case -- 5.3 The N=2 Wess-Zumino Model on Mell -- 5.4 Other Models -- Appendix A Self-adjoint Extensions of a Symmetric Operator Matrix
001450505 506__ $$aAccess limited to authorized users.
001450505 520__ $$aThis book explains the mathematical structures of supersymmetric quantum field theory (SQFT) from the viewpoints of functional and infinite-dimensional analysis. The main mathematical objects are infinite-dimensional Dirac operators on the abstract BosonFermion Fock space. The target audience consists of graduate students and researchers who are interested in mathematical analysis of quantum fields, including supersymmetric ones, and infinite-dimensional analysis. The major topics are the clarification of general mathematical structures that some models in the SQFT have in common, and the mathematically rigorous analysis of them. The importance and the relevance of the subject are that in physics literature, supersymmetric quantum field models are only formally (heuristically) considered and hence may be ill-defined mathematically. From a mathematical point of view, however, they suggest new aspects related to infinite-dimensional geometry and analysis. Therefore, it is important to show the mathematical existence of such models first and then study them in detail. The book shows that the theory of the abstract BosonFermion Fock space serves this purpose. The analysis developed in the book also provides a good example of infinite-dimensional analysis from the functional analysis point of view, including a theory of infinite-dimensional Dirac operators and Laplacians.
001450505 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed October 31, 2022).
001450505 650_0 $$aQuantum field theory$$xMathematics.
001450505 655_0 $$aElectronic books.
001450505 77608 $$iPrint version: $$z9811956774$$z9789811956775$$w(OCoLC)1335113799
001450505 830_0 $$aSpringerBriefs in mathematical physics ;$$vv. 46.
001450505 852__ $$bebk
001450505 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-981-19-5678-2$$zOnline Access$$91397441.1
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