137 research outputs found
Vacuum Energy as Spectral Geometry
Quantum vacuum energy (Casimir energy) is reviewed for a mathematical audience as a topic in spectral theory. Then some one-dimensional systems are solved exactly, in terms of closed classical paths and periodic orbits. The relations among local spectral densities, energy densities, global eigenvalue densities, and total energies are demonstrated. This material provides background and motivation for the treatment of higher-dimensional systems (self-adjoint second-order partial differential operators) by semiclassical approximation and other methods
Quantum Stability of Accelerated Black Holes
We study quantum aspects of the accelerated black holes in some detail.
Explicitly shown is the fact that a uniform acceleration stabilizes certain
charged black holes against the well-known thermal evaporation. Furthermore, a
close inspection of the geometry reveals that this is possible only for
near-extremal black holes and that most nonextremal varieties continue to
evaporate with a modified spectrum under the acceleration. We also introduce a
two-dimensional toy model where the energy-momentum flow is easily obtained for
general accelerations, and find the behavior to be in accordance with the
four-dimensional results. After a brief comparison to the classical system of a
uniformly accelerated charge, we close by pointing out the importance of this
result in the WKB expansion of the black hole pair-creation rate.Comment: LaTeX, 22 pages, 5 uuencoded figures (minor errors corrected, more
discussions on the case with black holes formed by gravitational collapse.
Four dimensional R^4 superinvariants through gauge completion
We fully compute the N=1 supersymmetrization of the fourth power of the Weyl
tensor in d=4 x-space with the auxiliary fields. In a previous paper, we showed
that their elimination requires an infinite number of terms; we explicitely
compute those terms to order \kappa^4 (three loop). We also write, in
superspace notation, all the possible N=1 actions, in four dimensions, that
contain pure R^4 terms (with coupling constants). We explicitely write these
actions in terms of the \theta components of the chiral density \epsilon and
the supergravity superfields R, G_m, W_{ABC}. Using the method of gauge
completion, we compute the necessary \theta components which allow us to write
these actions in x-space. We discuss under which circumstances can these extra
R^4 correction terms be reabsorbed in the pure supergravity action, and their
relevance to the quantum supergravity/string theory effective actions.Comment: 20 pages, no figures. Sec. 3 clarified; typos correcte
Comment on: "The Casimir force on a piston in the spacetime with extra compactified dimensions" [Phys. Lett. B 668 (2008) 72]
We offer a clarification of the significance of the indicated paper of H.
Cheng. Cheng's conclusions about the attractive nature of Casimir forces
between parallel plates are valid beyond the particular model in which he
derived them; they are likely to be relevant to other recent literature on the
effects of hidden dimensions on Casimir forces.Comment: 6 pages, 1 figur
On the Particle Definition in the presence of Black Holes
A canonical particle definition via the diagonalisation of the Hamiltonian
for a quantum field theory in specific curved space-times is presented. Within
the provided approach radial ingoing or outgoing Minkowski particles do not
exist. An application of this formalism to the Rindler metric recovers the
well-known Unruh effect. For the situation of a black hole the Hamiltonian
splits up into two independent parts accounting for the interior and the
exterior domain, respectively. It turns out that a reasonable particle
definition may be accomplished for the outside region only. The Hamiltonian of
the field inside the black hole is unbounded from above and below and hence
possesses no ground state. The corresponding equation of motion displays a
linear global instability. Possible consequences of this instability are
discussed and its relations to the sonic analogues of black holes are
addressed. PACS-numbers: 04.70.Dy, 04.62.+v, 10.10.Ef, 03.65.Db.Comment: 44 pages, LaTeX, no figures, accepted for publication in Phys. Rev.
Analytic approximation and an improved method for computing the stress-energy of quantized scalar fields in Robertson-Walker spacetimes
An improved method is given for the computation of the stress-energy tensor
of a quantized scalar field using adiabatic regularization. The method works
for fields with arbitrary mass and curvature coupling in Robertson-Walker
spacetimes and is particularly useful for spacetimes with compact spatial
sections. For massless fields it yields an analytic approximation for the
stress-energy tensor that is similar in nature to those obtained previously for
massless fields in static spacetimes.Comment: RevTeX, 8 pages, no figure
Cosmological backreaction of a quantized massless scalar field
We consider the backreaction problem of a quantized minimally coupled
massless scalar field in cosmology. The adiabatically regularized stress-energy
tensor in a general Friedmann-Robertson-Walker background is approximately
evaluated by using the fact that subhorizon modes evolve adiabatically and
superhorizon modes are frozen. The vacuum energy density is verified to obey a
new first order differential equation depending on a dimensionless parameter of
order unity, which calibrates subhorizon/superhorizon division. We check the
validity of the approximation by calculating the corresponding vacuum energy
densities in fixed backgrounds, which are shown to agree with the known results
in de Sitter space and space-times undergoing power law expansions. We then
apply our findings to slow-roll inflationary models. Although backreaction
effects are found to be negligible during the near exponential expansion, the
vacuum energy density generated during this period might be important at later
stages since it decreases slower than radiation or dust.Comment: 20 pages, 2 figures, v2: comments and a reference added, to appear in
JCA
The gravitational path integral and trace of the diffeomorphisms
I give a resolution of the conformal mode divergence in the Euclidean
gravitational path-integral by isolating the trace of the diffeomorphisms and
its contribution to the Faddeev-Popov measure.Comment: 20 pgs
The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes
Quantum fields propagating on a curved spacetime are investigated in terms of
microlocal analysis. We discuss a condition on the wave front set for the
corresponding n-point distributions, called ``microlocal spectrum condition''
(SC). On Minkowski space, this condition is satisfied as a consequence of
the usual spectrum condition. Based on Radzikowski's determination of the wave
front set of the two-point function of a free scalar field, satisfying the
Hadamard condition in the Kay and Wald sense, we construct in the second part
of this paper all Wick polynomials including the energy-momentum tensor for
this field as operator valued distributions on the manifold and prove that they
satisfy our microlocal spectrum condition.Comment: 21 pages, AMS-LaTeX, 2 figures appended as Postscript file
Quantum corrections to the noncommutative kink
We calculate quantum corrections to the mass of noncommutative phi^4 kink in
(1+1) dimensions for intermediate and large values of the noncommutativity
parameter theta. All one-loop divergences are removed by a mass renormalization
(which is different from the one required in the topologically trivial sector).
For large theta quantum corrections to the mass grow linearly with theta
signaling about possible break down of the perturbative expansion.Comment: 18 pages, v2: minor change
- …