1202.4117 (Ray J. Rivers)

Path Integrals for (Complex) Classical and Quantum Mechanics    [PDF]

Ray J. Rivers

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 $\hbar$ 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.

View original: http://arxiv.org/abs/1202.4117