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Compact and Noncompact Gauge Theories on a Lattice | Synapse

March 5, 2026Open Access

Compact and Noncompact Gauge Theories on a Lattice

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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Authors

B

Becchi C. M.

P

Palumbo F.

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Cite this study

M. et al. (Wed,) studied this question.

www.synapsesocial.com/papers/69a91dedd6127c7a504c14ef — DOI: https://doi.org/10.15161/oar.it/7zqzy-cwe91