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(Fermionic) mass meets (intrinsic) curvature

✍ Scribed by Jürgen Tolksdorf

Book ID: 104343235
Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 104 KB
Volume: 48
Category: Article
ISSN: 0393-0440
DOI: 10.1016/s0393-0440(03)00051-2

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✦ Synopsis

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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(Bosonic)mass meets (extrinsic)curvature

✍ Jürgen Tolksdorf 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 179 KB

In this paper, we discuss the mechanism of spontaneous symmetry breaking from the point view of vacuum pairs, considered as ground states of a Yang-Mills-Higgs gauge theory. We treat a vacuum as a section in an appropriate bundle that is naturally associated with a minimum of a (general) Higgs poten