2002/05/28 by Romulus Breban, Breban, Romulus
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Dimension (graph theory) #FOS: Physical sciences #Foliation (geology) #Formalism (music) #Imaginary time #Massless particle #Mathematics #Metric (unit) #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum mechanics #Quantum statistical mechanics #Space time #Supersymmetric quantum mechanics #Theoretical physics #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0205177
published in arXiv (Cornell University) (Cornell University) · Contains 22 pages and 4 figures. The manuscript was accepted for publication in Progress of Theoretical Physics. Typos were corrected in the current version
openalex publication_date 2002/05/28 · arxiv created 2015/03/19 · arxiv updated 2015/03/20 · openalex created_date 2025/10/27 · openalex updated_date 2026/08/06
We consider a five dimensional (5D) space-time with a space-like fifth\ndimension. We implement a quantum formalism by path integrals, and postulate\nthat all the physical information on a 5D massless particle propagation is\nprovided by the statistics over null paths in this 5D space-time. If the 5D\nmetric is independent of the fifth coordinate, then the propagation problem can\nbe reduced to four dimensions by foliation along the fifth coordinate, and we\nobtain a formulation of 4D Quantum Mechanics. If the 5D metric is independent\nof time, we foliate along the time coordinate, and obtain a formulation of 4D\nStatistical Mechanics. If the 5D metric is independent of both time and the\nfifth coordinate, then Quantum and Statistical Mechanics are pictures of the\nsame 5D reality. We also discuss the foliation of a proper space dimension, the\nKlein-Gordon equation, and a 5D Special Relativity, completing our\ninterpretation of the 5D geometry.\n