Jump to ContentJump to Main Navigation
The Conceptual Framework of Quantum Field Theory$
Users without a subscription are not able to see the full content.

Anthony Duncan

Print publication date: 2012

Print ISBN-13: 9780199573264

Published to Oxford Scholarship Online: January 2013

DOI: 10.1093/acprof:oso/9780199573264.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see http://www.oxfordscholarship.com/page/privacy-policy).date: 19 June 2018

Dynamics VII: Interacting fields: general aspects

Dynamics VII: Interacting fields: general aspects

Chapter:
(p.240) 9 Dynamics VII: Interacting fields: general aspects
Source:
The Conceptual Framework of Quantum Field Theory
Author(s):

Anthony Duncan

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199573264.003.0009

This chapter deals with the intricacies of interacting field theories, emphasizing very general aspects common to all local quantum field theories (LQFTs). The basic concept here is that of the interpolating Heisenberg field in terms of which the dynamics of the theory is specified, but which may be connected in various ways to the actual physical particle states. At this point, a characteristic feature of LQFTs becomes apparent: namely, the absence of any preferred, one-to-one connection between particles and fields. The discussion of field theory in the Heisenberg picture is first carried out in an ‘heuristic’ fashion, ignoring some important mathematical fine points; and then from a rigorous axiomatic point of view, starting with the Wightman axioms (spectral and field); and proceeding, via the Haag–Ruelle formulation of scattering theory, to the asymptotic formalism of Lehmann, Symanzik, and Zimmermann. The latter is treated in some detail, as it is central to subsequent discussions of the nature of the state space of field theory. The chapter also discusses the spectral properties of field theory, and the connection between the internal dynamics as specified by the interpolating fields and the phenomenological content of the theory as encapsulated in the asymptotic particle states and the S-matrix.

Keywords:   local quantum field theory, Heisenberg representation, Wightman axioms, Haag–Ruelle scattering theory, asymptotic formalism, Lehmann, Symanzik, and Zimmermann, spectral properties, particle states

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 .