Ultralocal quantum field theory in terms of currents - I. The free theory

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Abstract

The paper considers the possibility of constructing ultralocal theories, whose Hamiltonians contain no gradient terms and are therefore diagonal in position space, entirely in terms of currents with an equal time current algebra replacing the canonical commutation relations. It is shown that the free current theory can be defined in terms of a certain representation of the current algebra related to the group, S L(2, R). This representation is then constructed by using certain results of Araki and in the process a new infinitely divisible state on the universal covering group of SL(2, R) is displayed. An ultralocal free theory can also be constructed for the canonical fields, and its relation to the free current theory is shown to involve a certain renormalization procedure reminiscent of the thermodynamic limit.

Original languageEnglish (US)
Pages (from-to)169-204
Number of pages36
JournalCommunications in Mathematical Physics
Volume26
Issue number3
DOIs
StatePublished - Sep 1972

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current algebra
Quantum Field Theory
Current Algebra
commutation
coverings
Canonical Commutation Relations
Gradient Term
Infinitely Divisible
gradients
thermodynamics
Thermodynamic Limit
Renormalization
Covering

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

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Ultralocal quantum field theory in terms of currents - I. The free theory. / Newman, Charles.

In: Communications in Mathematical Physics, Vol. 26, No. 3, 09.1972, p. 169-204.

Research output: Contribution to journalArticle

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