  The essence of the path integral method in quantum physics can be expressed
in terms of two relations between unitary propagators, describing perturbations
of the underlying system. They inherit the causal structure of the theory and
its invariance properties under variations of the action. These relations
determine a dynamical algebra of bounded operators which encodes all properties
of the corresponding quantum theory. This novel approach is applied to
non-relativistic particles, where quantum mechanics emerges from it. The method
works also in interacting quantum field theories and sheds new light on the
foundations of quantum physics.
