The quantum mechanics of a single relativistic particle is a useful toy model for Einstein's General Relativity, as it exhibits a single reparametrization invariance which mimics part of the diffeomorphism invariance of GR. Spacetime coarse grainings--sets of alternatives defined with respect to a region extended in time as well as space--are of interest as a generalization of the usual alternatives defined on spacelike slices, since the the notion of ``spacelike'' is ill-defined in a theory where the metric itself is behaving quantum-mechanically. Spacetime coarse grainings were first proposed by Feynman [Rev Mod Phys 20, 367 (1948)], and have been examined in generalized quantum mechanics by Yamada and Takagi [Prog Theor Phys 87, 77 (1992); 85, 985 (1991)86, 599 (1991)] and Hartle [Phys Rev D44, 3173 (1991)]. This work studies spacetime coarse grainings in the generalized quantum mechanics of a relativistic particle.
This has been published in Phys Rev D50, 6344 (1994). Essentially the same paper is available as a preprint from the XXX e-print database at Los Alamos. There is also a condensed version from the 1994 Marcel Grossman proceedings.
Last Modified: 2009 September 8
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.
