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Quantum Field Theory and Critical Phenomena$
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Jean Zinn-Justin

Print publication date: 2002

Print ISBN-13: 9780198509233

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198509233.001.0001

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Quantum Field Theory: Functional Methods and Perturbation Theory

Quantum Field Theory: Functional Methods and Perturbation Theory

Chapter:
(p.145) 7 QUANTUM FIELD THEORY: FUNCTIONAL METHODS AND PERTURBATION THEORY
Source:
Quantum Field Theory and Critical Phenomena
Author(s):

JEAN ZINN-JUSTIN

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198509233.003.0007

This chapter proceeds with the study of local, relativistic quantum field theory. It first discusses the neutral self-coupled scalar field φ(x) introduced in Section 6.6.1. An important example is provided by the so-called φ4 theory, which has the theory of spinless bosons interacting through pair potentials, described in Section 5.5.4, as a non-relativistic limit. The chapter constructs a representation of the quantum statistical operator in the form of a functional integral, relativistic extension of the functional integrals introduced in Section 5.5.2. It then mainly investigates the simpler zero temperature limit where all d coordinates, euclidean time and space, can be treated symmetrically.

Keywords:   functional integrals, spinless bosons, quantum statistical operator

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