Infinite-Dimensional Dirac Operators and Supersymmetric Quantum Fields: An Introduction to Analysis on Boson-Fermion Fock Spaces

ISBN-13: 9789811956775 / Angielski / Miękka / 2022

Asao Arai

Opis

This 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 Boson–Fermion 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 Boson–Fermion 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.

Recenzje

"The book under review is a well-organized readable text in mathematical studies of supersymmetric quantum field theory. ... The book is almost self-contained." (Farhang Loran, Mathematical Reviews, June, 2023)

Spis treści

1. Boson Fock Space and Bose Field.- 2. Fermion Fock Space and Fermi Field.- 3. Boson-Fermion Fock Space and Supersymmetric Quantum Fields.- 4. Applications to Models in Supersymmetric Quantum Field Theory.

O autorze

Professor Asao Arai is a Professor Emeritus of Hokkaido University.