Path Integrals for (Complex) Classical and Quantum Mechanics

Authors

  • R. J. Rivers

DOI:

https://doi.org/10.14311/1414

Keywords:

phase space, path integral, complex classical physics

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 redolent of quantum mechanics; additional dimensions permit ‘tunnelling’ without recourse to instantons and time/energy uncertainties exist. In practice, ‘classical’ particle trajectories with additional degrees of freedom arise 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 ℏ 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.

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Published

2011-01-04

How to Cite

Rivers, R. J. (2011). Path Integrals for (Complex) Classical and Quantum Mechanics. Acta Polytechnica, 51(4). https://doi.org/10.14311/1414

Issue

Section

Articles