Koopmanvon Neumann formulation of classical YangMills theories: I
Abstract
In this paper we present the Koopmanvon Neumann (KvN) formulation of classical nonAbelian gauge field theories. In particular we shall explore the functional (or classical path integral) counterpart of the KvN method. In the quantum path integral quantization of YangMills theories concepts like gaugefixing and FaddeevPopov determinant appear in a quite natural way. We will prove that these same objects are needed also in this classical path integral formulation for YangMills theories. We shall also explore the classical path integral counterpart of the BFV formalism and build all the associated universal and gauge charges. These last are quite different from the analog quantum ones and we shall show the relation between the two. This paper lays the foundation of this formalism which, due to the many auxiliary fields present, is rather heavy. Applications to specific topics outlined in the paper will appear in later publications.
 Publication:

Annalen der Physik
 Pub Date:
 March 2006
 DOI:
 10.1002/andp.200510177
 arXiv:
 arXiv:hepth/0508244
 Bibcode:
 2006AnP...518..177C
 Keywords:

 Classical path integral;
 YangMills theories;
 High Energy Physics  Theory
 EPrint:
 46 pages, Latex