A non-canonical approach to arithmetic spin geometry and physical applications
type: Item
instance of: scholarly article
title: A non-canonical approach to arithmetic spin geometry and physical applications
zbMATH Open document ID: 1255.14013
DOI: 10.1134/S2070046610020056
author: René Schmidt
published in: \(p\)-Adic Numbers, Ultrametric Analysis, and Applications
publication date: 2012-11-13T00:00:00Z
review text: From the text: 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. In order to provide the basis for a number field invariant formulation of full Yang-Mills theory in the arithmetic geometric setting, we have to develop some mathematical tools. We will develop a non-canonical approach to arithmetic spin geometry which has a great deal in common with the classical differential geometric spin geometry, and which is particularly suited for physical applications. We perform the construction of the algebraic geometric analogue of associated bundle drawing inspiration from the differential geometric theory. [\dots] We will conclude that any connection on a torsor canonically gives rise to a connection on an associated object. The process of reduction of the structure group is available in the arithmetic setting too.
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 14D21
Mathematics Subject Classification ID: 14G25
Mathematics Subject Classification ID: 81T13
zbMATH DE Number: 6105040
zbMATH Keywords: torsor
zbMATH Keywords: associated bundle
zbMATH Keywords: Yang-Mills theory
MaRDI profile type: Publication
cites work: THE WAVE FUNCTION OF THE UNIVERSE AND p-ADIC GRAVITY
cites work: Q3997794
cites work: Algebraic spaces
cites work: Q5731354
cites work: Q4530238
cites work: Q4003475
cites work: Number theory as the ultimate physical theory
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description: scientific article; zbMATH DE number 6105040