# Quantum mechanics and field theory with momentum defined on an anti-de-Sitter space - High Energy Physics - Theory

Quantum mechanics and field theory with momentum defined on an anti-de-Sitter space - High Energy Physics - Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: Relativistic dynamics with energy and momentum resricted to an anti-de-Sitterspace is presented, specifically in the introduction of coordiate operatorsconjugate to such momenta. Definition of functions of these operators, theirdifferentiation and integration, all necessary for the development of dynamicsis presented. The resulting algebra differs from the standard Heisenberg one,notably in that the space-time coordinates do not commute among each other. Theresulting time variable is discrete and the limit to continuous time presentsdifficulties. A parallel approach, in which an overlap function, betweenposition and momentum states, is obtained from solutions of wave equations onthis curved space are also investigated. This approach, likewise, has problemsin the that high energy behavior of these overlap functions precludes aspace-time definition of action functionals.

Author: ** Myron Bander**

Source: https://arxiv.org/