Functional integrals and inequivalent representations in Quantum Field Theory

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Functional integrals and inequivalent representations in Quantum Field Theory

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Functional integrals and inequivalent representations in Quantum Field Theory

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10303 - Particles and field physics

Projekt

<a href="/cs/project/GF17-33812L" target="_blank" >GF17-33812L: Informačně-teoretický přístup ke komplexním dynamickým systémům</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Annals of Physics

ISSN

0003-4916

e-ISSN

1096-035X

Svazek periodika

383

Číslo periodika v rámci svazku

Aug

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

32

Strana od-do

207-238

Kód UT WoS článku

000407667300013

EID výsledku v databázi Scopus

2-s2.0-85033451161