http://xxx.lanl.gov/list/gr-qc/
gr-qc/0005133 [abs, src, ps, other] :
Title: Vacuum Energy Density Fluctuations in Minkowski and Casimir States via
Smeared Quantum Fields and Point Separation
Authors: Nicholas. G. Phillips, B. L. Hu
Comments: 41 pages, 2 figures
We present calculations of the variance of fluctuations and of the mean of
the energy momentum tensor of a massless scalar field for the Minkowski and
Casimir vacua as a function of an intrinsic scale defined by a smeared field
or by point separation. We point out that contrary to prior claims, the ratio
of variance to mean-squared being of the order unity is not necessarily a
good criterion for measuring the invalidity of semiclassical gravity. For the
Casimir topology we obtain expressions for the variance to mean-squared ratio
as a function of the intrinsic scale (defined by a smeared field) compared to
the extrinsic scale (defined by the separation of the plates, or the
periodicity of space). Our results make it possible to identify the spatial
extent where negative energy density prevails which could be useful for
studying quantum field effects in worm holes and baby universe, and for
examining the design feasibility of real-life `time-machines'.
For the Minkowski vacuum we find that the ratio of the variance to the
mean-squared, calculated from the coincidence limit, is identical to the
value of the Casimir case at the same limit for spatial point separation
while identical to the value of a hot flat space result with a temporal
point-separation. We analyze the origin of divergences in the fluctuations of
the energy density and discuss choices in formulating a procedure for their
removal, thus raising new questions into the uniqueness and even the very
meaning of regularization of the energy momentum tensor for quantum fields in
curved or even flat spacetimes when spacetime is viewed as having an extended
structure. (50kb
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