Multi-Time Wave Functions versus Multiple Timelike Dimensions

Abstract

Multi-time wave functions are wave functions for multi-particle quantum systems that involve several time variables (one per particle). In this paper we contrast them with solutions of wave equations on a space-time with multiple timelike dimensions, i.e., on a pseudo-Riemannian manifold whose metric has signature such as $++--$ or $++------$, instead of $+---$. Despite the superficial similarity, the two behave very differently: Whereas wave equations in multiple timelike dimensions are typically mathematically ill-posed and presumably unphysical, relevant Schrödinger equations for multi-time wave functions possess for every initial datum a unique solution on the spacelike configurations and form a natural covariant representation of quantum states.

10 pages, 1 figure; peer-reviewed version accepted for publication in Foundations of Physics

References in corpus (1)

• A relativistically interacting exactly solvable multi-time model for two mass-less Dirac particles in 1+1 dimensions