Abstract:
The matrix elements of the evolution operator of interacting bosons and fermions are represented as path integrals over coherent states on a Lie group. In the case of spinless electrons interacting with the electromagnetic field, this integral is transformed to an integral over the paths of the electrons in the three-dimensional space $E_3$. A scheme for constructing a path integral for electrons with spin degrees of freedom is proposed.
Citation:
L. F. Novikov, “Path integral over a $c$-number measure for interacting bosons and fermions”, TMF, 54:2 (1983), 193–208; Theoret. and Math. Phys., 54:2 (1983), 123–133