Abstract
We consider a classical gauge theory on a principal fiber bundle P → X in the case where its structure group G is reduced to a subgroup H in the presence of classical Higgs fields described by global sections of the quotient fiber bundle P/H → X. We show that matter fields with the exact symmetry group H in such a theory are described by sections of the composition fiber bundle Y → P/H → X, where Y → P/H is the fiber bundle with the structure group H, and the Lagrangian of these sections is factored by virtue of the vertical covariant differential determined by a connection on the fiber bundle Y → P/H.
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This paper is dedicated to the 75th birthday of Academician of the RAS A. A. Slavnov
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 181, No. 3, pp. 553–567, December, 2014.
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Sardanashvily, G.A. Classical higgs fields. Theor Math Phys 181, 1599–1611 (2014). https://doi.org/10.1007/s11232-014-0238-y
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DOI: https://doi.org/10.1007/s11232-014-0238-y