Path Integrals for (Complex) Classical and Quantum Mechanics
Abstract
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to instantons and lead to time/energy uncertainty. In practice, 'classical' particle trajectories with additional degrees of freedom have arisen in several different formulations of quantum mechanics. In this talk we compare the extended phase space of the closed time-path formalism with that of complex classical mechanics, to suggest that has a role in our understanding of the latter. However, differences in the way that trajectories are used make a deeper comparison problematical. We conclude with some thoughts on quantisation as dimensional reduction.
Cite
@article{arxiv.1202.4117,
title = {Path Integrals for (Complex) Classical and Quantum Mechanics},
author = {Ray J. Rivers},
journal= {arXiv preprint arXiv:1202.4117},
year = {2012}
}
Comments
13 pages: Published in the Proceedings of AAMP 7, (Prague) 2011. This file differs from the published version by the inclusion of extra references, with minor changes of text (which leave conclusions unaltered)