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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

Quantum Field Theory and Critical Phenomena


Oxford University Press

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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