1,612 research outputs found
Quasilocal Conservation Laws: Why We Need Them
We argue that conservation laws based on the local matter-only
stress-energy-momentum tensor (characterized by energy and momentum per unit
volume) cannot adequately explain a wide variety of even very simple physical
phenomena because they fail to properly account for gravitational effects. We
construct a general quasi}local conservation law based on the Brown and York
total (matter plus gravity) stress-energy-momentum tensor (characterized by
energy and momentum per unit area), and argue that it does properly account for
gravitational effects. As a simple example of the explanatory power of this
quasilocal approach, consider that, when we accelerate toward a freely-floating
massive object, the kinetic energy of that object increases (relative to our
frame). But how, exactly, does the object acquire this increasing kinetic
energy? Using the energy form of our quasilocal conservation law, we can see
precisely the actual mechanism by which the kinetic energy increases: It is due
to a bona fide gravitational energy flux that is exactly analogous to the
electromagnetic Poynting flux, and involves the general relativistic effect of
frame dragging caused by the object's motion relative to us.Comment: 20 pages, 1 figur
Geoids in General Relativity: Geoid Quasilocal Frames
We develop, in the context of general relativity, the notion of a geoid -- a
surface of constant "gravitational potential". In particular, we show how this
idea naturally emerges as a specific choice of a previously proposed, more
general and operationally useful construction called a quasilocal frame -- that
is, a choice of a two-parameter family of timelike worldlines comprising the
worldtube boundary of the history of a finite spatial volume. We study the
geometric properties of these geoid quasilocal frames, and construct solutions
for them in some simple spacetimes. We then compare these results -- focusing
on the computationally tractable scenario of a non-rotating body with a
quadrupole perturbation -- against their counterparts in Newtonian gravity (the
setting for current applications of the geoid), and we compute
general-relativistic corrections to some measurable geometric quantities.Comment: 24 pages, 8 figures; v2: reference added; v3: introduction clarified,
reference adde
Dirac versus Reduced Quantization of the Poincar\'{e} Symmetry in Scalar Electrodynamics
The generators of the Poincar\'{e} symmetry of scalar electrodynamics are
quantized in the functional Schr\"{o}dinger representation. We show that the
factor ordering which corresponds to (minimal) Dirac quantization preserves the
Poincar\'{e} algebra, but (minimal) reduced quantization does not. In the
latter, there is a van Hove anomaly in the boost-boost commutator, which we
evaluate explicitly to lowest order in a heat kernel expansion using zeta
function regularization. We illuminate the crucial role played by the gauge
orbit volume element in the analysis. Our results demonstrate that preservation
of extra symmetries at the quantum level is sometimes a useful criterion to
select between inequivalent, but nevertheless self-consistent, quantization
schemes.Comment: 24 page
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