Commutativity of substitution and variation in the actions of quantum field theory

Zhong Chao Wu
Phys. Rev. D 80, 105001 – Published 3 November 2009

Abstract

There exists a paradox in quantum field theory: substituting a field configuration, which solves a subset of the field equations into the action, and varying it is not necessarily equivalent to substituting that configuration into the remaining field equations. We take the S4 and Freund-Rubin–like instantons as two examples to clarify the paradox. One must match the specialized configuration field variables with the corresponding boundary conditions by adding appropriate Legendre terms to the action. Some comments are made regarding exceptional degenerate cases.

  • Received 28 July 2009

DOI:https://doi.org/10.1103/PhysRevD.80.105001

©2009 American Physical Society

Authors & Affiliations

Zhong Chao Wu*

  • Department of Physics, Zhejiang University of Technology, Hangzhou, Zhejiang 310032, China

  • *zcwu2007@yahoo.com

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 80, Iss. 10 — 15 November 2009

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×