Jump to ContentJump to Main Navigation
Quantum Field Theory and Critical Phenomena$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 26 January 2021

Quantum Evolution: From Particles To Fields

Quantum Evolution: From Particles To Fields

Quantum Field Theory and Critical Phenomena


Oxford University Press

To calculate scattering S-matrix elements, quantities relevant to Particle Physics, it is necessary to consider instead the quantum evolution operator in real time. This chapter begins by deriving the path integral representation of the evolution operator and the S-matrix in simple quantum mechanics. To illustrate the power of the formalism, it shows how to recover the perturbative expansion of the scattering amplitude, some semi-classical approximations, and the eikonal approximation. When the asymptotic states at large time are eigenstates of the harmonic oscillator, instead of free particles, the holomorphic formalism becomes useful. A simple generalization of the path integral of Section 5.1 leads to the corresponding path integral representation of the S-matrix. In the case of the Bose gas the evolution operator is then given by a holomorphic functional integral. Using the parallel formalism of Section 5.6, the chapter derives an analogous representation for the evolution operator of a system of non-relativistic fermions. It then begins the study of relativistic quantum field theory with the example of the self-coupled neutral scalar boson. It shows that the holomorphic formalism, in a form that extends the construction of Section 5.5 to relativistic real time evolution, leads to various representations of the S-matrix in terms of functional integrals. The chapter relates S-matrix elements to the continuation to real time of various kinds of euclidean correlation functions.

Keywords:   S-matrix, quantum evolution operator, functional integrals, quantum field theory, holomorphic formalism, quantum mechanics

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .