(Fermionic)Mass Meets (Intrinsic)Curvature

Details (Fermionic)Mass Meets (Intrinsic)Curvature (Fermionic)Mass Meets (Intrinsic)Curvature

2002-12-05

arxiv.org/abs/math-ph/0212021v1

Physics

Mathematical Physics

14 pages

Scientific paper

10.1016/S0393-0440(03)00051-2

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.

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