16,649 research outputs found
Quantized Maxwell Theory in a Conformally Invariant Gauge
Maxwell theory can be studied in a gauge which is invariant under conformal
rescalings of the metric, and first proposed by Eastwood and Singer. This paper
studies the corresponding quantization in flat Euclidean 4-space. The resulting
ghost operator is a fourth-order elliptic operator, while the operator P on
perturbations of the potential is a sixth-order elliptic operator. The operator
P may be reduced to a second-order non-minimal operator if a dimensionless
gauge parameter tends to infinity. Gauge-invariant boundary conditions are
obtained by setting to zero at the boundary the whole set of perturbations of
the potential, jointly with ghost perturbations and their normal derivative.
This is made possible by the fourth-order nature of the ghost operator. An
analytic representation of the ghost basis functions is also obtained.Comment: 8 pages, plain Tex. In this revised version, the calculation of ghost
basis functions has been amended, and the presentation has been improve
Essential self-adjointness in one-loop quantum cosmology
The quantization of closed cosmologies makes it necessary to study squared
Dirac operators on closed intervals and the corresponding quantum amplitudes.
This paper proves self-adjointness of these second-order elliptic operators.Comment: 14 pages, plain Tex. An Erratum has been added to the end, which
corrects section
Boundary Operators in Quantum Field Theory
The fundamental laws of physics can be derived from the requirement of
invariance under suitable classes of transformations on the one hand, and from
the need for a well-posed mathematical theory on the other hand. As a part of
this programme, the present paper shows under which conditions the introduction
of pseudo-differential boundary operators in one-loop Euclidean quantum gravity
is compatible both with their invariance under infinitesimal diffeomorphisms
and with the requirement of a strongly elliptic theory. Suitable assumptions on
the kernel of the boundary operator make it therefore possible to overcome
problems resulting from the choice of purely local boundary conditions.Comment: 23 pages, plain Tex. The revised version contains a new section, and
the presentation has been improve
Quantum Effects in Friedmann-Robertson-Walker Cosmologies
Electrodynamics for self-interacting scalar fields in spatially flat
Friedmann-Robertson-Walker space-times is studied. The corresponding one-loop
field equation for the expectation value of the complex scalar field in the
conformal vacuum is derived. For exponentially expanding universes, the
equations for the Bogoliubov coefficients describing the coupling of the scalar
field to gravity are solved numerically. They yield a non-local correction to
the Coleman-Weinberg effective potential which does not modify the pattern of
minima found in static de Sitter space. Such a correction contains a
dissipative term which, accounting for the decay of the classical configuration
in scalar field quanta, may be relevant for the reheating stage. The physical
meaning of the non-local term in the semiclassical field equation is
investigated by evaluating this contribution for various background field
configurations.Comment: 17 pages, plain TeX + 5 uuencoded figure
Non-Local Boundary Conditions in Euclidean Quantum Gravity
Non-local boundary conditions for Euclidean quantum gravity are proposed,
consisting of an integro-differential boundary operator acting on metric
perturbations. In this case, the operator P on metric perturbations is of
Laplace type, subject to non-local boundary conditions; by contrast, its
adjoint is the sum of a Laplacian and of a singular Green operator, subject to
local boundary conditions. Self-adjointness of the boundary-value problem is
correctly formulated by looking at Dirichlet-type and Neumann-type realizations
of the operator P, following recent results in the literature. The set of
non-local boundary conditions for perturbative modes of the gravitational field
is written in general form on the Euclidean four-ball. For a particular choice
of the non-local boundary operator, explicit formulae for the boundary-value
problem are obtained in terms of a finite number of unknown functions, but
subject to some consistency conditions. Among the related issues, the problem
arises of whether non-local symmetries exist in Euclidean quantum gravity.Comment: 23 pages, plain Tex. The revised version is much longer, and new
original calculations are presented in section
Euclidean Maxwell Theory in the Presence of Boundaries. II
Zeta-function regularization is applied to complete a recent analysis of the
quantized electromagnetic field in the presence of boundaries. The quantum
theory is studied by setting to zero on the boundary the magnetic field, the
gauge-averaging functional and hence the Faddeev-Popov ghost field. Electric
boundary conditions are also studied. On considering two gauge functionals
which involve covariant derivatives of the 4-vector potential, a series of
detailed calculations shows that, in the case of flat Euclidean 4-space bounded
by two concentric 3-spheres, one-loop quantum amplitudes are gauge independent
and their mode-by-mode evaluation agrees with the covariant formulae for such
amplitudes and coincides for magnetic or electric boundary conditions. By
contrast, if a single 3-sphere boundary is studied, one finds some
inconsistencies, i.e. gauge dependence of the amplitudes.Comment: 24 pages, plain-tex, recently appearing in Classical and Quantum
Gravity, volume 11, pages 2939-2950, December 1994. The authors apologize for
the delay in circulating the file, due to technical problems now fixe
Non-Locality and Ellipticity in a Gauge-Invariant Quantization
The quantum theory of a free particle in two dimensions with non-local
boundary conditions on a circle is known to lead to surface and bulk states.
Such a scheme is here generalized to the quantized Maxwell field, subject to
mixed boundary conditions. If the Robin sector is modified by the addition of a
pseudo-differential boundary operator, gauge-invariant boundary conditions are
obtained at the price of dealing with gauge-field and ghost operators which
become pseudo-differential. A good elliptic theory is then obtained if the
kernel occurring in the boundary operator obeys certain summability conditions,
and it leads to a peculiar form of the asymptotic expansion of the symbol. The
cases of ghost operator of negative and positive order are studied within this
framework.Comment: 17 pages, plain Te
One-Loop Divergences in Simple Supergravity: Boundary Effects
This paper studies the semiclassical approximation of simple supergravity in
Riemannian four-manifolds with boundary, within the framework of
-function regularization. The massless nature of gravitinos, jointly
with the presence of a boundary and a local description in terms of potentials
for spin , force the background to be totally flat. First, nonlocal
boundary conditions of the spectral type are imposed on spin-
potentials, jointly with boundary conditions on metric perturbations which are
completely invariant under infinitesimal diffeomorphisms. The axial
gauge-averaging functional is used, which is then sufficient to ensure
self-adjointness. One thus finds that the contributions of ghost and gauge
modes vanish separately. Hence the contributions to the one-loop wave function
of the universe reduce to those values resulting from physical modes
only. Another set of mixed boundary conditions, motivated instead by local
supersymmetry and first proposed by Luckock, Moss and Poletti, is also
analyzed. In this case the contributions of gauge and ghost modes do not cancel
each other. Both sets of boundary conditions lead to a nonvanishing
value, and spectral boundary conditions are also studied when two concentric
three-sphere boundaries occur. These results seem to point out that simple
supergravity is not even one-loop finite in the presence of boundaries.Comment: 37 pages, Revtex. Equations (5.2), (5.3), (5.5), (5.7), (5.8) and
(5.13) have been amended, jointly with a few misprint
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