Group-theoretical derivation of a path integral

The dynamics of nonrelativistic particle formulated in terms of the Feynman path integral is derived from the group-theoretical considerations. The group-theoretical approach is applied, which allows us to develop qUantum theory of elementary particle from the given symmetry group. In this approach quantUm properties of a particle result from intertwining of two special representations of the symmetry group, one of the representations describing local properties of the particle and the other one describing the particle as a whole (its global properties). The appoach is applied to the generalised Galilei semigroup obtained from the Galilei group by means of changing the translation group into the semigroup of trajectories (parametrised paths). As a result, the propagator of a particle in an external electromagnetic or gauge field is derived in the form of a path integral. The measure of path integration including the weight factor exp (iS) is determined by the invariance condition