THE HOLONOMY GROUP AND SPONTANEOUS SYMMETRY BREAKING

Ross, D.K.

doi:10.1063/1.525438

THE HOLONOMY GROUP AND SPONTANEOUS SYMMETRY BREAKING

D.K. Ross
(
- Iowa State U.
)

1982

4 pages

Published in:

J.Math.Phys. 23 (1982) 869-872

DOI:

10.1063/1.525438

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Abstract: (AIP)

We show that the residual symmetry group after spontaneous symmetry breaking must either be the holonomy group H of the connection or contain H as a subgroup. Since H is a connected, normal Lie subgroup of the gauge group G, knowing the dimension of H is often sufficient to determine H itself. We develop an algorithm for determining dim H for any gauge theory given the structure constants of the gauge group. This algorithm is then applied to a fiber bundle with an SU2 or SU3 gauge group.

SPONTANEOUS SYMMETRY BREAKING
GROUP THEORY: LIE
FIELD THEORY: FIBRE BUNDLE
group: SU(2)
group: SU(3)
TRANSFORMATION: GAUGE

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