452 research outputs found
Groups with the Minimal Conditions for Subgroups and for Nonabelian Subgroups
For some very wide classes and
of groups, the author proves that an
arbitrary (nonabelian) group (respectively ) satisfies the minimal condition for (nonabelian) subgroups iff
it is Cherniko
Inflaton Decay in an Alpha Vacuum
We study the alpha vacua of de Sitter space by considering the decay rate of
the inflaton field coupled to a scalar field placed in an alpha vacuum. We find
an {\em alpha dependent} Bose enhancement relative to the Bunch-Davies vacuum
and, surprisingly, no non-renormalizable divergences. We also consider a
modified alpha dependent time ordering prescription for the Feynman propagator
and show that it leads to an alpha independent result. This result suggests
that it may be possible to calculate in any alpha vacuum if we employ the
appropriate causality preserving prescription.Comment: 16 pages, 1 figure, Revtex 4 preprin
Localized Particle States and Dynamics Gravitational Effects
Scalar particles--i.e., scalar-field excitations--in de Sitter space exhibit
behavior unlike either classical particles in expanding space or quantum
particles in flat spacetime. Their energies oscillate forever, and their
interactions are spread out in energy. Here it is shown that these features
characterize not only normal-mode excitations spread out over all space, but
localized particles or wave packets as well. Both one-particle and coherent
states of a massive, minimally coupled scalar field in de Sitter space,
associated with classical wave packets, are constructed explicitly. Their
energy expectation values and corresponding Unruh-DeWitt detector response
functions are calculated. Numerical evaluation of these quantities for a simple
set of classical wave packets clearly displays these novel features. Hence,
given the observed accelerating expansion of the Universe, it is possible that
observation of an ultralow-mass scalar particle could yield direct confirmation
of distinct predictions of quantum field theory in curved spacetime.Comment: 12 pages, 5 figure
Energy Density in Expanding Universes as Seen by Unruh's Detector
We consider the response of an Unruh detector to scalar fields in an
expanding space-time. When combining transition elements of the scalar field
Hamiltonian with the interaction operator of detector and field, one finds at
second order in time-dependent perturbation theory a transition amplitude,
which actually dominates in the ultraviolet over the first order contribution.
In particular, the detector response faithfully reproduces the particle number
implied by the stress-energy of a minimally coupled scalar field, which is
inversely proportional to the energy of a scalar mode. This finding disagrees
with the contention that in de Sitter space, the response of the detector drops
exponentially with particle energy and therefore indicates a thermal spectrum.Comment: 15 pages, 1 figur
De Sitter Breaking through Infrared Divergences
Just because the propagator of some field obeys a de Sitter invariant
equation does not mean it possesses a de Sitter invariant solution. The classic
example is the propagator of a massless, minimally coupled scalar. We show that
the same thing happens for massive scalars with , and for massive
transverse vectors with , where is the dimension
of spacetime and is the Hubble parameter. Although all masses in these
ranges give infrared divergent mode sums, using dimensional regularization (or
any other analytic continuation technique) to define the mode sums leads to the
incorrect conclusion that de Sitter invariant solutions exist except at
discrete values of the masses.Comment: 27 pages, no figures, uses LaTeX 2epsilo
Transforming to Lorentz Gauge on de Sitter
We demonstrate that certain gauge fixing functionals cannot be added to the
action on backgrounds such as de Sitter in which a linearization instability is
present. We also construct the field dependent gauge transformation which
carries the electromagnetic vector potential from a convenient, non-de Sitter
invariant gauge to the de Sitter invariant, Lorentz gauge. The transformed
propagator agrees with the de Sitter invariant result previously found by
solving the propagator equation in Lorentz gauge. This shows that the gauge
transformation technique will eliminate unphysical breaking of de Sitter
invariance introduced by a gauge condition. It is suggested that the same
technique can be used to finally resolve the issue of whether or not free
gravitons are de Sitter invariant.Comment: 45 page
The Coincidence Limit of the Graviton Propagator in de Donder Gauge on de Sitter Background
We explicitly work out the de Sitter breaking contributions to the recent
solution for the de Donder gauge graviton propagator on de Sitter. We also
provide explicit power series expansions for the two structure functions, which
are suitable for implementing dimensional regularization. And we evaluate the
coincidence limit of the propagator.Comment: 41 pages, uses LaTeX 2e, version 2 has some typoes correcte
Theory of gravitation theories: a no-progress report
Already in the 1970s there where attempts to present a set of ground rules,
sometimes referred to as a theory of gravitation theories, which theories of
gravity should satisfy in order to be considered viable in principle and,
therefore, interesting enough to deserve further investigation. From this
perspective, an alternative title of the present paper could be ``why are we
still unable to write a guide on how to propose viable alternatives to general
relativity?''. Attempting to answer this question, it is argued here that
earlier efforts to turn qualitative statements, such as the Einstein
Equivalence Principle, into quantitative ones, such as the metric postulates,
stand on rather shaky grounds -- probably contrary to popular belief -- as they
appear to depend strongly on particular representations of the theory. This
includes ambiguities in the identification of matter and gravitational fields,
dependence of frequently used definitions, such as those of the stress-energy
tensor or classical vacuum, on the choice of variables, etc. Various examples
are discussed and possible approaches to this problem are pointed out. In the
course of this study, several common misconceptions related to the various
forms of the Equivalence Principle, the use of conformal frames and equivalence
between theories are clarified.Comment: Invited paper in the Gravity Research Foundation 2007 special issue
to be published by Int. J. Mod. Phys.
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