Diffeomorphism groups in quantum theory and statistical physics

Research output: Chapter in Book/Report/Conference proceedingChapter


Symmetry groups describe invariances or partial invariances in physical systems under transformations. Locality refers to the association between physical effects and spatial or spacetime regions, with “action at a distance” forbidden. Local symmetry joins these ideas mathematically in the theory of certain infinite-dimensional groups and their representations. This chapter is an extended abstract of lectures by the author, surveying how unitary representations of diffeomorphism groups and the corresponding current algebras provide a unifying framework for understanding or predicting a wide variety of different quantum and statistical systems.

Original languageEnglish (US)
Title of host publicationTrends in Mathematics
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages6
StatePublished - 2020

Publication series

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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • Cocycles
  • Configuration spaces
  • Diffeomorphism groups
  • Infinite-dimensional groups
  • Locality
  • Quantum statistics
  • Quasi-invariant measures
  • Statistical physics
  • Symmetry
  • Unitary representations


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