The Canonical Operator in Many-Particle Problems and Quantum Field Theory

Victor P. Maslov; Oleg Yu. Shvedov

Published by De Gruyter 2022

The Canonical Operator in Many-Particle Problems and Quantum Field Theory

Victor P. Maslov and Oleg Yu. Shvedov

Volume 71 in the series De Gruyter Expositions in Mathematics

https://doi.org/10.1515/9783110762709

Overview
Contents

About this book

In this monograph we study the problem of construction of asymptotic solutions of equations for functions whose number of arguments tends to infinity as the small parameter tends to zero. Such equations arise in statistical physics and in quantum theory of a large number of fi elds. We consider the problem of renormalization of quantum field theory in the Hamiltonian formalism, which encounters additional difficulties related to the Stückelberg divergences and the Haag theorem. Asymptotic methods for solving pseudodifferential equations with small parameter multiplying the derivatives, as well as the asymptotic methods developed in the present monograph for solving problems in statistical physics and quantum field theory, can be considered from a unified viewpoint if one introduces the notion of abstract canonical operator. The book can be of interest for researchers – specialists in asymptotic methods, statistical physics, and quantum fi eld theory as well as for graduate and undergraduate students of these specialities.

Develops a new asymptotic method which allows one to construct approximations for functions of large number of arguments. Discusses how to construct to construct a new axiomatics of relativistic quantum field theory.

Author / Editor information

V. P. Maslov, MIEM/HSE School of Applied Mathematics, Russia; O. Y. Shvedov, Lomonosov Moscow State University, Russia.

Topics

Frontmatter Publicly Available Download PDF	I
Preface to the English edition Publicly Available Download PDF	VII
Preface Publicly Available Download PDF	XI
Contents Publicly Available Download PDF	XIX
List of notation Publicly Available Download PDF	XXVII
1 Abstract canonical operator and symplectic geometry Requires Authentication Unlicensed Licensed Download PDF	1
2 Multiparticle canonical operator and its properties Requires Authentication Unlicensed Licensed Download PDF	61
3 Asymptotic solutions of the many-body problem Requires Authentication Unlicensed Licensed Download PDF	139
4 Complex germ method in the Fock space Requires Authentication Unlicensed Licensed Download PDF	193
5 Asymptotic methods in problems with operator-valued symbol Requires Authentication Unlicensed Licensed Download PDF	299
6 Semiclassical field theory in the Hamiltonian formalism Requires Authentication Unlicensed Licensed Download PDF	331
7 Asymptotic methods for systems of a large number of fields Requires Authentication Unlicensed Licensed Download PDF	403
Concluding remarks Requires Authentication Unlicensed Licensed Download PDF	439
Bibliography Requires Authentication Unlicensed Licensed Download PDF	443
Index Requires Authentication Unlicensed Licensed Download PDF	447

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Graduate students and researchers specializing in asymptotic methods in statistical physics and quantum field theory.
Pages
- Front matter: 28
- Main content: 450
Keywords: Kanonische; Asymptotische; Mathematik

eBook

Published: June 21, 2022
ISBN: 9783110762709

Hardcover

Published: June 21, 2022
ISBN: 9783110762389