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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.