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 8Dr. John T. Whelan / email@example.com / Professor, School of Mathematical Sciences & Center for Computational Relativity and Gravitation, Rochester Institute of Technology
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