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Classical Higgs fields. (English. Russian original) Zbl 1317.81273

Theor. Math. Phys. 181, No. 3, 1599-1611 (2014); translation from Teor. Mat. Fiz. 181, No. 3, 553-567 (2014).
Summary: We consider a classical gauge theory on a principal fiber bundle \(P \to X\) 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 \(P/H \to X\). We show that matter fields with the exact symmetry group \(H\) in such a theory are described by sections of the composition fiber bundle \(Y \to P/H \to X\), where \(Y \to P/H\) 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 \(Y \to P/H\).

MSC:

81V22 Unified quantum theories
14D06 Fibrations, degenerations in algebraic geometry
81T13 Yang-Mills and other gauge theories in quantum field theory
81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
55R91 Equivariant fiber spaces and bundles in algebraic topology
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References:

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