The Canonical Operator in ManyParticle Problems and Quantum Field Theory
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...
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Format:  eBook 
Language:  English 
Published: 
Berlin ; Boston
De Gruyter
2022, ©2022

Series:  De Gruyter Expositions in Mathematics

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Collection:  DeGruyter MPG Collection  Collection details see MPG.ReNa 
Summary:  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. 

Physical Description:  XXVI, 448 pages 
ISBN:  9783110762709 9783110762747 