1,811 research outputs found
Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir Problem
The Casimir problem is usually posed as the response of a fluctuating quantum
field to externally imposed boundary conditions. In reality, however, no
interaction is strong enough to enforce a boundary condition on all frequencies
of a fluctuating field. We construct a more physical model of the situation by
coupling the fluctuating field to a smooth background potential that implements
the boundary condition in a certain limit. To study this problem, we develop
general new methods to compute renormalized one--loop quantum energies and
energy densities. We use analytic properties of scattering data to compute
Green's functions in time--independent background fields at imaginary momenta.
Our calculational method is particularly useful for numerical studies of
singular limits because it avoids terms that oscillate or require cancellation
of exponentially growing and decaying factors. To renormalize, we identify
potentially divergent contributions to the Casimir energy with low orders in
the Born series to the Green's function. We subtract these contributions and
add back the corresponding Feynman diagrams, which we combine with counterterms
fixed by imposing standard renormalization conditions on low--order Green's
functions. The resulting Casimir energy and energy density are finite
functionals for smooth background potentials. In general, however, the Casimir
energy diverges in the boundary condition limit. This divergence is real and
reflects the infinite energy needed to constrain a fluctuating field on all
energy scales; renormalizable quantum field theories have no place for ad hoc
surface counterterms. We apply our methods to simple examples to illustrate
cases where these subtleties invalidate the conclusions of the boundary
condition approach.Comment: 36pages, Latex, 20 eps files. included via epsfi
Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms
Let and be two integers with , and let and be
integers with and . In this paper, we prove that , where is a constant depending on and .Comment: 8 pages. To appear in Archiv der Mathemati
Experimental study of ultracold neutron production in pressurized superfluid helium
We have investigated experimentally the pressure dependence of the production
of ultracold neutrons (UCN) in superfluid helium in the range from saturated
vapor pressure to 20bar. A neutron velocity selector allowed the separation of
underlying single-phonon and multiphonon pro- cesses by varying the incident
cold neutron (CN) wavelength in the range from 3.5 to 10{\AA}. The predicted
pressure dependence of UCN production derived from inelastic neutron scattering
data was confirmed for the single-phonon excitation. For multiphonon based UCN
production we found no significant dependence on pressure whereas calculations
from inelastic neutron scattering data predict an increase of 43(6)% at 20bar
relative to saturated vapor pressure. From our data we conclude that applying
pressure to superfluid helium does not increase the overall UCN production rate
at a typical CN guide.Comment: 18 pages, 8 figures Version accepted for publication in PR
Energy-Momentum Restrictions on the Creation of Gott Time Machines
The discovery by Gott of a remarkably simple spacetime with closed timelike
curves (CTC's) provides a tool for investigating how the creation of time
machines is prevented in classical general relativity. The Gott spacetime
contains two infinitely long, parallel cosmic strings, which can equivalently
be viewed as point masses in (2+1)-dimensional gravity. We examine the
possibility of building such a time machine in an open universe. Specifically,
we consider initial data specified on an edgeless, noncompact, spacelike
hypersurface, for which the total momentum is timelike (i.e., not the momentum
of a Gott spacetime). In contrast to the case of a closed universe (in which
Gott pairs, although not CTC's, can be produced from the decay of stationary
particles), we find that there is never enough energy for a Gott-like time
machine to evolve from the specified data; it is impossible to accelerate two
particles to sufficiently high velocity. Thus, the no-CTC theorems of Tipler
and Hawking are enforced in an open (2+1)-dimensional universe by a mechanism
different from that which operates in a closed universe. In proving our result,
we develop a simple method to understand the inequalities that restrict the
result of combining momenta in (2+1)-dimensional gravity.Comment: Plain TeX, 41 pages incl. 9 figures. MIT-CTP #225
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