Abstract
The study of the Weyl and Dirac topological materials (topological semimetals, insulators, superfluids and superconductors) opens the route for the investigation of the topological quantum vacua of relativistic fields. The symmetric phase of the standard model (SM), where both electroweak and chiral symmetry are not broken, represents the topological semimetal. The vacua of the SM (and its extensions) in the phases with broken electroweak symmetry represent the topological insulators of different types. We discuss in detail the topological invariants in both the symmetric and broken phases and establish their relation to the stability of vacuum.
Highlights
The massless Weyl fermions in the symmetric phase of the standard model (SM) of fundamental interactions have common topological properties with the Weyl and Dirac fermions in topological semimetals
Under this limit the topological classes of the SM vacua are classified according to the topological invariant associated with the matrix of CT symmetry, which protects the number of massive Dirac fermions
We demonstrate that in the noninteracting case of the massive SM Dirac fermions the value of the symmetry protected topological invariant associated with T is equal to zero, NKT = 0
Summary
The study of the Weyl and Dirac topological materials (topological semimetals, insulators, superfluids this work must maintain and superconductors) opens the route for the investigation of the topological quantum vacua of attribution to the author(s) and the title of relativistic fields. The symmetric phase of the standard model (SM), where both electroweak and chiral the work, journal citation and DOI. Symmetry are not broken, represents the topological semimetal. The vacua of the SM (and its extensions) in the phases with broken electroweak symmetry represent the topological insulators of different types. We discuss in detail the topological invariants in both the symmetric and broken phases and establish their relation to the stability of vacuum
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