Infinite-dimensional Dirac operators and supersymmetric quantum fields : an introduction to analysis on Boson-Fermion Fock spaces / / Asao Arai

• Record Nr.: UNISA996495169303316
• Autore: Arai Asao
• Pubbl/distr/stampa: Singapore : , : Springer, , [2022]; ©2022
• ISBN: 9789811956782; 9789811956775
• Descrizione fisica: 1 online resource (123 pages)
• Collana: SpringerBriefs in Mathematical Physics ; ; v.46
• Disciplina: 610
• Soggetti: Quantum field theory; Teoria quàntica de camps; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Includes index.
• Nota di contenuto: Intro -- 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 -- 2.2 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 -- 3.4 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 -- 4.5.3 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) -- 4.12.1 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 -- Appendix B Construction of an Infinite-Dimensional Gaussian Measure on a Path Space -- Appendix References -- -- Index.