International Journal of Theoretical Physics
, Volume 4, Issue 4, pp 247265
First online:
Phase space, fibre bundles and current algebras
 Basil J. HileyAffiliated withDepartment of Physics, Birkbeck College, University of London
 , Allan E. G. StuartAffiliated withDepartment of Mathematics, The City University
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The purpose of this paper is to extend into phase space the cellular description introduced by Bohmet al. (1970) and to show how this may help to give an understanding of the current algebra approach to elementary particle phenomena. We investigate this cellular structure in phase space in some detail and show how certain features of the structure may be described in terms of the mathematics of fibre bundle theory. The frame bundle is discussed and compared with the YangMills theory. As a result of this discussion we are able to introduce generalised currents which are related to the duals of the curvature forms, and these are shown to span the Lie algebra of a subgroup of the structure group of the frame bundle. We then discuss the implications of these results in terms of our cell structure. By assuming that the de Rahm cohomology, defined by the curvature forms and their duals, reflect a cohomology on the integers defined on the original cell structure, we show that the currents and ‘curvature’ can be given a meaning in terms of a discrete structure. In this case the currents only span a Lie algebra in some suitable limit, implying that a description using Lie algebras is only an approximation.
 Title
 Phase space, fibre bundles and current algebras
 Journal

International Journal of Theoretical Physics
Volume 4, Issue 4 , pp 247265
 Cover Date
 197108
 DOI
 10.1007/BF00674278
 Print ISSN
 00207748
 Online ISSN
 15729575
 Publisher
 Kluwer Academic PublishersPlenum Publishers
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 Authors

 Basil J. Hiley ^{(1)}
 Allan E. G. Stuart ^{(2)}
 Author Affiliations

 1. Department of Physics, Birkbeck College, University of London, Malet Street, London W.C.1
 2. Department of Mathematics, The City University, London