Multi-Time Wave Functions Versus Multiple Timelike Dimensions

作者：Lienert Matthias^*; Petrat Soren; Tumulka Roderich

来源：Foundations of Physics, 2017, 47(12): 1582-1590.

DOI：10.1007/s10701-017-0120-5

• Relativistic quantum theory
• Lorentz invariance
• Pseudo-Riemannian metric
• Existence of solutions
• Ultrahyperbolic equation

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 ++-- 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 Schrodinger 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.

• 出版日期2017-12
• 单位rutgers