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March 5, 20260 citationsOpen Access

Compact and Noncompact Gauge Theories on a Lattice

BMBecchi C. M.PFPalumbo F.

Key Points

  • The aim is to investigate a noncompact formulation of gauge theories on the lattice and its implications for representations of the gauge group.
  • Analysis of a noncompact gauge theory formulation on a lattice
  • Examination of the representations of the SU(2) gauge group
  • Use of gauge-invariant constraints to eliminate auxiliary fields
  • Demonstrated that the SU(2) gauge group representation is completely reducible
  • Identified one irreducible multiplet containing Yang-Mills fields and an auxiliary field
  • Showed how eliminating the auxiliary field leads to Wilson's formulation

Abstract

A noncompact formulation of gauge theories on the lattice recently proposed makes use of auxiliary fields. We show that in such a formulation the representation of the gauge group in the case of SU(2) is completely reducible, one of the irreducible multiplets containing the Yang-Mills fields plus one auxiliary field. Elimination of this field by a gauge-invariant constraint leads to Wilson's formulation.

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Cite This Study

M. et al. (1991) studied this question.

synapsesocial.com/papers/69a91dedd6127c7a504c14efhttps://doi.org/10.15161/oar.it/7zqzy-cwe91
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