Narrow Results

We obtain the Schrödinger wave functions of a generalized pendulum under time-dependent gravitation by making use of the Lewis and Riesenfeld invariant method. As an example, we consider a generalized pendulum with constant gravitation and exponentially increasing mass. We also present a canonical approach to the generalized time-dependent pendulum.

In this paper, we explore the perspectives for canonical simulations in the worldline formulation of a lattice field theory. Using the charged ${\varphi }^4$ field in two dimensions as an example, we present the details of the canonical formulation based on worldlines and outline the algorithmic strategies for canonical worldline simulations. We discuss the steps for converting the data from the canonical approach to the grand canonical picture which we use for cross-checking our results. The canonical approach presented here can easily be generalized to other lattice field theories with a worldline representation.