(Fermionic) mass meets (intrinsic) curvature

[摘要] Using the notion of vacuum pairs we show how the (square of the) mass matrix of the fermions can be considered geometrically as curvature. This curvature together with the curvature of space-time, defines the total curvature of the Clifford module bundle representing a free fermion within the geometrical setup of spontaneously broken Yang-Mills-Higgs gauge theories. The geometrical frame discussed here gives rise to a natural class of Lagrangian densities. It is shown that the geometry of the Clifford module bundle representing a free fermion is described by a canonical spectral invariant Lagrangian density. (C) 2003 Elsevier Science B.V. All rights reserved.

[发布日期] 2003-11-01

[关键词] geometrization;fermionic mass matrix;Clifford module bundles;spontaneously broken gauge symmetry