Diffeomorphism group representations in relativistic quantum field theory

Gerald A. Goldin, David H. Sharp

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations


We explore the role played by the diffeomorphism group and its unitary representations in relativistic quantum field theory. From the quantum kinematics of particles described by representations of the diffeomorphism group of a space-like surface in an inertial reference frame, we reconstruct the local relativistic neutral scalar field in the Fock representation. An explicit expression for the free Hamiltonian is obtained in terms of the Lie algebra generators (mass and momentum densities). We suggest that this approach can be generalized to fields whose quanta are spatially extended objects.

Original languageEnglish (US)
Title of host publicationTrends in Mathematics
PublisherSpringer International Publishing
Number of pages10
StatePublished - 2019

Publication series

NameTrends in Mathematics
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • Diffeomorphism groups
  • Relativistic quantum fields
  • Unitary group representations


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