A path-integral approach to the problem of time

2016/01/31 by M. M. Amaral, M.M. Amaral, Martin Bojowald
Mathematics · Physics and Astronomy · #Amplitude #Intuition #Path integral formulation #Point (geometry) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Transition time #gr-qc #hep-th

paper · pdf · doi:10.1016/j.aop.2017.11.027

published as Annals of Physics 388C (2018) 241-266 · 19 pages, v2: additional remarks on topological turning points

arxiv created 2016/02/07 · openalex created_date 2016/06/24 · openalex publication_date 2017/11/24 · arxiv updated 2017/12/19 · openalex updated_date 2026/08/06

Abstract

Quantum transition amplitudes are formulated for a model system with local internal time, using path integrals. The amplitudes are shown to be more regular near a turning point of internal time than could be expected based on existing canonical treatments. In particular, a successful transition through a turning point is provided in the model system, together with a new definition of such a transition in general terms. Some of the results rely on a fruitful relation between the problem of time and general Gribov problems.

Citations

• Quantization of non-Abelian gauge theories
• Generalized Hamiltonian Dynamics
• Spin foam quantization and anomalies
• Applications of a new proposal for solving the ‘‘problem of time’’ to some simple quantum cosmological models