1,113 research outputs found
Classical and Quantum Implications of the Causality Structure of Two-Dimensional Spacetimes with Degenerate Metrics
The causality structure of two-dimensional manifolds with degenerate metrics
is analysed in terms of global solutions of the massless wave equation. Certain
novel features emerge. Despite the absence of a traditional Lorentzian Cauchy
surface on manifolds with a Euclidean domain it is possible to uniquely
determine a global solution (if it exists), satisfying well defined matching
conditions at the degeneracy curve, from Cauchy data on certain spacelike
curves in the Lorentzian region. In general, however, no global solution
satisfying such matching conditions will be consistent with this data.
Attention is drawn to a number of obstructions that arise prohibiting the
construction of a bounded operator connecting asymptotic single particle
states. The implications of these results for the existence of a unitary
quantum field theory are discussed.Comment: 27 pages LaTex (6 Figures), Journal of Mathematical Physics
(Accepted
Gauge Symmetry and Gravito-Electromagnetism
A tensor description of perturbative Einsteinian gravity about an arbitrary
background spacetime is developed. By analogy with the covariant laws of
electromagnetism in spacetime, gravito-electromagnetic potentials and fields
are defined to emulate electromagnetic gauge transformations under
substitutions belonging to the gauge symmetry group of perturbative
gravitation. These definitions have the advantage that on a flat background,
with the aid of a covariantly constant timelike vector field, a subset of the
linearised gravitational field equations can be written in a form that is fully
analogous to Maxwell's equations (without awkward factors of 4 and extraneous
tensor fields). It is shown how the remaining equations in the perturbed
gravitational system restrict the time dependence of solutions to these
equations and thereby prohibit the existence of propagating vector fields. The
induced gravito-electromagnetic Lorentz force on a test particle is evaluated
in terms of these fields together with the torque on a small gyroscope. It is
concluded that the analogy of perturbative gravity to Maxwell's description of
electromagnetism can be valuable for (quasi-)stationary gravitational phenomena
but that the analogy has its limitations.Comment: 29 pages no-fig
Solutions for Neutral for Axi-Dilaton Gravity in 4-Dimensions
We examine a 1 parameter class of actions describing the gravitational
interaction between a pair of scalar fields and Einsteinian gravitation. When
the parameter is positive the theory corresponds to an axi-dilatonic sector of
low energy string theory. We exploit an SL(2,R) symmetry of the theory to
construct a family of electromagnetically neutral solutions with non-zero axion
and dilaton charge from solutions of the Brans-Dicke theory. We also comment on
solutions to the theory with negative coupling parameter.Comment: 7 pages Plain Tex (No Figures), Letter to Editor, Classical and
Quantum Gravit
Tensor distributions on signature-changing space-times
Irregularities in the metric tensor of a signature-changing space-time
suggest that field equations on such space-times might be regarded as
distributional. We review the formalism of tensor distributions on
differentiable manifolds, and examine to what extent rigorous meaning can be
given to field equations in the presence of signature-change, in particular
those involving covariant derivatives. We find that, for both continuous and
discontinuous signature-change, covariant differentiation can be defined on a
class of tensor distributions wide enough to be physically interesting.Comment: 9 pages, LaTeX 2.0
Twisted Electromagnetic Modes and Sagnac Ring-Lasers
A new approximation scheme, designed to solve the covariant Maxwell equations
inside a rotating hollow slender conducting cavity (modelling a ring-laser), is
constructed. It is shown that for well-defined conditions there exist TE and TM
modes with respect to the longitudinal axis of the cavity. A twisted mode
spectrum is found to depend on the integrated Frenet torsion of the cavity and
this in turn may affect the Sagnac beat frequency induced by a non-zero
rotation of the cavity. The analysis is motivated by attempts to use
ring-lasers to measure terrestrial gravito-magnetism or the Lense-Thirring
effect produced by the rotation of the Earth.Comment: LaTeX 31 pages, 3 Figure
Maxwell's Equations in a Uniformly Rotating Dielectric Medium and the Wilson-Wilson Experiment
This note offers a conceptually straightforward and efficient way to
formulate and solve problems in the electromagnetics of moving media based on a
representation of Maxwell's equations in terms of differential forms on
spacetime together with junction conditions at moving interfaces. This
framework is used to address a number of issues that have been discussed
recently in this journal about the theoretical description underlying the
interpretation of the Wilson-Wilson experiment.Comment: 16 pages, 2 figure
Quantum Electromagnetic Fluctuations in Inhomogeneous Dielectric Media
A new mathematical and computational technique for calculating quantum vacuum
expectation values of energy and momentum densities associated with
electromagnetic fields in bounded domains containing inhomogeneous media is
discussed. This technique is illustrated by calculating the mode contributions
to the difference in the vacuum force expectation between opposite ends of an
inhomogeneous dielectric non-dispersive medium confined to a perfectly
conducting rigid box.Comment: 7 pages, appeared in Proceedings of SPIE Conference on Quantum Optics
(2011
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