Geometrical approach to the reduction of gauge theories with spontaneously broken symmetry

Section: Historymentioning

confidence: 99%

Gauge gravitation theory: Gravity as a Higgs field

Sardanashvily

2016

“…In gauge theory on a principal bundle P → X, a symmetry breaking is defined as reduction of the structure Lie group G of this principal bundle to a closed (consequently, Lie) subgroup H of exact symmetries [22,38,54,63,67,74,83].…”

Section: Symmetry Breaking and Higgs Fieldsmentioning

confidence: 99%

Classical Field Theory: Advanced Mathematical Formulation

Sardanashvily

2008

“…P contains an H-principal subbundle called a G-structure [22,32,42,46,50]. We have the composite bundle…”

Section: Classical Gauge Theorymentioning

confidence: 99%

Preface

2008

The Higgs mechanism of mass generation is the main ingredient in the contemporary standard model of high energy physics and its various generalizations. The key point of this mechanism is interaction of particles and fields with a certain multiplet of Higgs fields associated to some gauge symmetry group and possessing nonzero vacuum expectations. The latter is treated as spontaneous symmetry breaking. The Higgs mechanism has been extended to different gauge theories including SUSY gauge theory [12,40,43,56], noncommutative field theory [19,39,44], gravitation theory [1,13,31,33,35], the gauge Landau-Ginzburg-Higgs theory [3,23]. In quantum field theory, spontaneous symmetry breaking phenomena imply that a physical vacuum is not the bare Fock one, but it possesses nonzero physical characteristics and, thus, can interact with particles and fields.At present, there is no comprehensive theory of spontaneous symmetry breaking. In order to attract attention to this problem, let us summarize the relevant mathematical results characterizing spontaneous symmetry breaking in algebraic quantum theory, axiomatic quantum field theory, group theory, and classical gauge theory. Int. J. Geom. Methods Mod. Phys. 2008.05:v-xvi. Downloaded from www.worldscientific.com by YALE UNIVERSITY on 07/18/15. For personal use only.