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Infinite-dimensional Dirac operators...

Arai, Asao.

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

Record Type:	Electronic resources : Monograph/item
Title/Author:	Infinite-dimensional Dirac operators and supersymmetric quantum fields/ by Asao Arai.
Reminder of title:	an introduction to analysis on Boson-Fermion Fock spaces /
Author:	Arai, Asao.
Published:	Singapore :Springer Nature Singapore : : 2022.,
Description:	xiii, 117 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Quantum field theory - Mathematics. -
Online resource:	https://doi.org/10.1007/978-981-19-5678-2
ISBN:	9789811956782

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

Infinite-dimensional Dirac operators and supersymmetric quantum fieldsan introduction to analysis on Boson-Fermion Fock spaces /[electronic resource] :by Asao Arai. - Singapore :Springer Nature Singapore :2022. - xiii, 117 p. :ill., digital ;24 cm. - SpringerBriefs in mathematical physics,v. 462197-1765 ;. - SpringerBriefs in mathematical physics ;v. 46..

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.

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.

ISBN: 9789811956782

Standard No.: 10.1007/978-981-19-5678-2doiSubjects--Topical Terms:

658956
Quantum field theory
--Mathematics.

LC Class. No.: QC174.45 / .A73 2022

Dewey Class. No.: 530.143

Infinite-dimensional Dirac operators and supersymmetric quantum fields = an introduction to analysis on Boson-Fermion Fock spaces /
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520 $a 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.
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