Integral Representations of Causal Commutators

Freeman J. Dyson
Phys. Rev. 110, 1460 – Published 15 June 1958
PDFExport Citation

Abstract

An integral representation is found for the matrix element, between given states, of the commutator of two field operators. The representation makes use of the information derivable from the local commutativity of the operators and from the mass spectrum of the fields. The representation was discovered by Jost and Lehmann and proved by them for the case of two fields of equal mass. It is here extended to the case of unequal masses.

The mathematical basis of this work is the fact that every function f(q) of a four-vector q, with a Fourier transform f̃(x) which vanishes for space like x, has a unique extension which is a solution of the wave equation in six dimensions.

  • Received 26 February 1958

DOI:https://doi.org/10.1103/PhysRev.110.1460

©1958 American Physical Society

Authors & Affiliations

Freeman J. Dyson

  • Institute for Advanced Study, Princeton, New Jersey

References (Subscription Required)

Click to Expand
Issue

Vol. 110, Iss. 6 — June 1958

Reuse & Permissions
Access Options

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Journals Archive

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×