PATH-INTEGRAL FOR SPIN - A NEW APPROACH

The path integral representation for the propagator of a Dirac particl e in an external electromagnetic field is derived using the functional derivative formalism with the help of Weyl symbol representation for the Grassmann vector part of the variables. The proposed method simpli fies the proof of the path integral representation starting from the e quation for the Green function significantly and automatically leads t o a precise and unambiguous set of boundary conditions for the anticom muting variables and puts strong restrictions on the choice of the gau ge conditions. The same problem is reconsidered using the Polyakov and Batalin-Fradkin-Vilkovisky methods together with the Weyl symbol meth od and it is shown to yield the same PIR. It is shown that in the last case, the non-trivial first class constraints algebra far a Dirac par ticle plays an important role in the derivation, and this algebra is t he limiting case of the superconformal algebra for a Ramond open strin g when the width goes to zero. That the approach proposed here can be applied to any point-like particle is illustrated in the propagator fo r the nonrelativistic Pauli spinning particle in an external electroma gnetic field.