Functional integrals and inequivalent representations in Quantum Field Theory
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F17%3A00312895" target="_blank" >RIV/68407700:21340/17:00312895 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.aop.2017.05.022" target="_blank" >http://dx.doi.org/10.1016/j.aop.2017.05.022</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aop.2017.05.022" target="_blank" >10.1016/j.aop.2017.05.022</a>
Alternative languages
Result language
angličtina
Original language name
Functional integrals and inequivalent representations in Quantum Field Theory
Original language description
We discuss canonical transformations in Quantum Field Theory in the framework of the functional-integral approach. In contrast with ordinary Quantum Mechanics, canonical transformations in Quantum Field Theory are mathematically more subtle due to the existence of unitarily inequivalent representations of canonical commutation relations. When one works with functional integrals, it is not immediately clear how this algebraic feature manifests itself in the formalism. Here we attack this issue by considering the canonical transformations in the context of coherent-state functional integrals. Specifically, in the case of linear canonical transformations, we derive the general functional-integral representations for both transition amplitude and partition function phrased in terms of new canonical variables. By means of this, we show how in the infinite-volume limit the canonical transformations induce a transition from one representation of canonical commutation relations to another one and under what conditions the representations are unitarily inequivalent. We also consider the partition function and derive the energy gap between statistical systems described in two different representations which, among others, allows to establish a connection with continuous phase transitions. We illustrate the inner workings of the outlined mechanism by discussing two prototypical systems: the van Hove model and the Bogoliubov model of weakly interacting Bose gas. (C) 2017 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10303 - Particles and field physics
Result continuities
Project
<a href="/en/project/GF17-33812L" target="_blank" >GF17-33812L: An information-theoretical perspective on complex systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Annals of Physics
ISSN
0003-4916
e-ISSN
1096-035X
Volume of the periodical
383
Issue of the periodical within the volume
Aug
Country of publishing house
US - UNITED STATES
Number of pages
32
Pages from-to
207-238
UT code for WoS article
000407667300013
EID of the result in the Scopus database
2-s2.0-85033451161