NEW APPROACH TO THE PATH-INTEGRAL REPRESENTATION FOR THE DIRAC PARTICLE PROPAGATOR

The path integral representation for the propagator of a spinning part icle in an external electromagnetic field is derived using the functio nal derivative formalism with the help of a Weyl symbol representation . The proposed method essentially simplifies the proof of the path int egral representation starting from the equation for the Green function and automatically leads to a precise and unambiguous form of the boun dary conditions for the Grassmann variables and puts a strong restrict ion on the choice of the gauge condition. The path integral representa tion as in the canonical case has been obtained from the general quant ization method of Batalin, Fradkin, and Vilkovisky employing a Weyl sy mbol representation; being the nontrivial first class constraint algeb ra for a Dirac particle plays an important role in this derivation. Th is algebra is the limiting case of the superconformal algebra for a Ra mond-type open string when the width of one goes to aero.