Remarks on some applications of Skorokhod space in quantum mechanics (Q2726273)

The present paper is a brief review of the use of the Skorokhod space and convergence of probability measures on it in some recent studies of quantum systems over fields and rings not only over the reals, but also over \(p\)- adic fields. The first application discussed is the approximation of usual quantum systems by finite quantum systems. The second is a discussion of a path integral formalism applicable to a class of \(p\)-adic Schrödinger equations; the corresponding probability measure comes from a stochastic process with independent increments and is defined on the Skorokhod space of functions on \([0, \infty)\) with values in a finite-dimensional vector space over a non-archimedean local field. This stochastic process and the associated measure therefore play the same role in the study of these \(p\)-adic Schrödinger equations as the Brownian motion in the theory of the usual Schrödinger equations.NEWLINENEWLINEFor the entire collection see [Zbl 0956.00022].