Erratum: Spontaneous symmetry breaking, gauge theories, the Higgs mechanism and all that

1975 ◽  
Vol 47 (1) ◽  
pp. 259-259
Author(s):  
Jeremy Bernstein
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Gauge Theories ◽  
Higgs Mechanism

scholarly journals Symmetry breaking via internal geometry

2005 ◽  
Vol 2005 (13) ◽  
pp. 2023-2030 ◽  
Author(s):  
Andrew Talmadge
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Principal Bundle ◽  
Gauge Theories ◽  
Higgs Mechanism ◽  
Internal Space ◽  
Hermitian Metric ◽  
Unitary Transformations ◽  
Vector Valued ◽  
Higgs Scalar

Gauge theories commonly employ complex vector-valued fields to reduce symmetry groups through the Higgs mechanism of spontaneous symmetry breaking. The geometry of the internal spaceVis tacitly assumed to be the metric geometry of some static, nondynamical hermitian metrick. In this paper, we considerG-principal bundle gauge theories, whereGis a subgroup ofU(V,k)(the unitary transformations on the internal vector spaceVwith hermitian metrick) and we consider allowing the hermitian metric on the internal spaceVto become an additional dynamical element of the theory. We find a mechanism for interpreting the Higgs scalar field as a feature of the geometry of the internal space while retaining the successful aspects of the Higgs mechanism and spontaneous symmetry breaking

Gauge hierarchies for chiral SU(N) × SU(N) groups

1976 ◽  
Vol 54 (16) ◽  
pp. 1660-1663 ◽  
Author(s):  
Shalom Eliezer
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Gauge Theories ◽  
Vacuum Expectation ◽  
Coupling Constants ◽  
Spontaneous Breaking ◽  
Text Representation ◽  
Algebraic Equations ◽  
Expectation Values ◽  
Special Case

We have presented a special case where a hierarchy of spontaneous breaking of the symmetries can be achieved in conventional gauge theories (i.e. the Higgs scalars are elementary bosons and the coupling constants of the quartic interactions are small). We break spontaneously the chiral group SU(N) × SU(N) with Higgs scalars transforming like the (N, [Formula: see text]) representation of SU(N) × SU(N). By minimizing the potential we obtain a set of algebraic equations of the type[Formula: see text]where ηj are the vacuum expectation values of the Higgs scalars and μi2 and Aij are parameters. In order to get a hierarchy of spontaneous symmetry breaking we obtain the condition det Aij = 0.

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