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Skeletonization is the procedure by which formal phase space path integrals are given concrete meaning in terms of a time slicing. This means replacing the action functional with a sum of functions of the values taken on consecutive time slicings. In configuration space, the skeletonized action is built out of the Hamilton principal function, but in phase space, there is an ambiguity in choosing the analogous phase space principal function (PSPF), which has tangible consequences on a sum-over-histories quantum theory. This work concerns one criterion for choosing a PSPF, based on the involution property, by which an extremization procedure can be used to remove intermediate points in the skeletonization.

This work is in progress, but there was a report on preliminary results given at the Seventh Canadian Conference on General Relativity and Relativistic Astrophysics. A writeup, to appear in the conference proceedings, is available as a preprint from the LANL XXX e-print database.

Last Modified: 2011 April 6

Dr. John T. Whelan / john.whelan@astro.rit.edu / Professor, School of Mathematical Sciences & Center for Computational Relativity and Gravitation, Rochester Institute of TechnologyThe contents of this communication are the sole responsibility of Prof. John T. Whelan and do not necessarily represent the opinions or policies of RIT, SMS, or CCRG.