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

Victor P. Maslov, Oleg Yu. Shvedov

• Publisher: De Gruyter
• Year: 2022
• Topic: Mathematics
• eBook ISBN:
  9783110762747
• Subtopic: Applied Mathematics
• Index: Mathematics

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.

Table of contents

• Title Page
• Copyright
• Contents
• Preface to the English edition
• 1 Abstract canonical operator and symplectic geometry
• 2 Multiparticle canonical operator and its properties
• 3 Asymptotic solutions of the many-body problem
• 4 Complex germ method in the Fock space
• 5 Asymptotic methods in problems with operator-valued symbol
• 6 Semiclassical field theory in the Hamiltonian formalism
• 7 Asymptotic methods for systems of a large number of fields
• Subject Index