Abstract Yang–Mills Theory

Anastasios Mallios ()
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Anastasios Mallios: University of Athens Panepistimioupolis, Department of Mathematics

Chapter 1 in Modern Differential Geometry in Gauge Theories, 2009, pp 3-77 from Springer

Abstract: Abstract The objects of our study in this chapter belong to what we may call the Yang–Mills category (see Section 4.2 for concrete definitions), while the corresponding morphisms are suitable connection-preserving sheaf morphisms (ibid. (4.16)). Now, since the necessary background material for the subject matter at issue has not been systematically developed so far, within the framework of abstract differential geometry (see A. Mallios [VS: Vols. I and II]), which is employed by the present treatise, we give below a detailed exposition of all the relevant issues that will be needed in the sequel. In this context, see also, however, A. Mallios [6: p. 164, Appendix II] for a brief account on the same material. Among the various standard presentations of this subject, see, for instance, T. Petrie–J. Randall [1]. So we start with the ensuing fundamental notions for all the subsequent discussion.

Keywords: Vector Sheaf; Mill Theory; Local Gauge; Structure Sheaf; Beltrami Operator (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/978-0-8176-4634-9_1

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