Multi-Time Wave Functions versus Multiple Timelike Dimensions
arXiv:1708.03376 · doi:10.1007/s10701-017-0120-5
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
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