A non-canonical approach to arithmetic spin geometry and physical applications

Abstract

A basic requirement of adelic physics is the principle of invariance of the fundamental physical laws under a change of the underlying number field proposed by I.V. Volovich (cf. [20]). In this paper, we develop a manifestly number field invariant approach to Yang-Mills theory, which is formulated within the framework of arithmetic geometry. As well source fields as the Higgs mechanism are incorporated. For this purpose a non-canonical approach to arithmetic spin geometry is proposed, and its physical applications are analyzed. The associated bundle construction is performed in the setting of arithmetic geometry. Furthermore the arithmetic analogue of the following well-known differential geometric fact is proven: Every covariant derivation on a torsor induces a canonical covariant derivation on the associated object.