1,302 research outputs found
Note on Signature Change and Colombeau Theory
Recent work alludes to various `controversies' associated with signature
change in general relativity. As we have argued previously, these are in fact
disagreements about the (often unstated) assumptions underlying various
possible approaches. The choice between approaches remains open.Comment: REVTex, 3 pages; to appear in GR
A New Look at the Ashtekar-Magnon Energy Condition
In 1975, Ashtekar and Magnon showed that an energy condition selects a unique
quantization procedure for certain observers in general, curved spacetimes. We
generalize this result in two important ways, by eliminating the need to assume
a particular form for the (quantum) Hamiltonian, and by considering the
surprisingly nontrivial extension to nonminimal coupling.Comment: REVTeX, 10 page
Distributional Modes for Scalar Field Quantization
We propose a mode-sum formalism for the quantization of the scalar field
based on distributional modes, which are naturally associated with a slight
modification of the standard plane-wave modes. We show that this formalism
leads to the standard Rindler temperature result, and that these modes can be
canonically defined on any Cauchy surface.Comment: 15 pages, RevTe
Quaternionic Spin
We rewrite the standard 4-dimensional Dirac equation in terms of quaternionic
2-component spinors, leading to a formalism which treats both massive and
massless particles on an equal footing. The resulting unified description has
the correct particle spectrum to be a generation of leptons, with the correct
number of spin/helicity states. Furthermore, precisely three such generations
naturally combine into an octonionic description of the 10-dimensional massless
Dirac equation, as discussed in previous work.Comment: LaTeX2e, 15 pages, 1 PS figure; to appear in Clifford '99 proceeding
Stochastic Tachyon Fluctuations, Marginal Deformations and Shock Waves in String Theory
Starting with exact solutions to string theory on curved spacetimes we obtain
deformations that represent gravitational shock waves. These may exist in the
presence or absence of sources. Sources are effectively induced by a tachyon
field that randomly fluctuates around a zero condensate value. It is shown that
at the level of the underlying conformal field theory (CFT) these deformations
are marginal and moreover all \a'-corrections are taken into account. Explicit
results are given when the original undeformed 4-dimensional backgrounds
correspond to tensor products of combinations of 2-dimensional CFT's, for
instance SL(2,R)/R \times SU(2)/U(1).Comment: 26 pages, harvmac, no figures. Very minor modifications, and in
addition conditions (B.3) and (B.4) were also obtained using beta-function
equations. Version to appear in Phys. Rev.
Eikonal Particle Scattering and Dilaton Gravity
Approximating light charged point-like particles in terms of (nonextremal)
dilatonic black holes is shown to lead to certain pathologies in Planckian
scattering in the eikonal approximation, which are traced to the presence of a
(naked) curvature singularity in the metric of these black holes. The existence
of such pathologies is confirmed by analyzing the problem in an `external
metric' formulation where an ultrarelativistic point particle scatters off a
dilatonic black hole geometry at large impact parameters. The maladies
disappear almost trivially upon imposing the extremal limit. Attempts to derive
an effective three dimensional `boundary' field theory in the eikonal limit are
stymied by four dimensional (bulk) terms proportional to the light-cone
derivatives of the dilaton field, leading to nontrivial mixing of
electromagnetic and gravitational effects, in contrast to the case of general
relativity. An eikonal scattering amplitude, showing decoupling of these
effects, is shown to be derivable by resummation of graviton, dilaton and
photon exchange ladder diagrams in a linearized version of the theory, for an
asymptotic value of the dilaton field which makes the string coupling constant
non-perturbative.Comment: 22 pages, Revte
Diffeomorphism algebra of two dimensional free massless scalar field with signature change
We study a model of free massless scalar fields on a two dimensional cylinder
with metric that admits a change of signature between Lorentzian and Euclidean
type (ET), across the two timelike hypersurfaces (with respect to Lorentzian
region). Considering a long strip-shaped region of the cylinder, denoted by an
angle \theta, as the signature changed region it is shown that the energy
spectrum depends on the angle \theta and in a sense differs from ordinary one
for low energies. Morever diffeomorphism algebra of corresponding infinite
conserved charges is different from '' Virasoro'' algebra and approaches to it
at higher energies. The central term is also modified but does not approach to
the ordinary one at higher energies.Comment: 18 pages, Latex, 2 ps figure
Dynamical Determination of the Metric Signature in Spacetime of Nontrivial Topology
The formalism of Greensite for treating the spacetime signature as a
dynamical degree of freedom induced by quantum fields is considered for
spacetimes with nontrivial topology of the kind , for varying . It is shown that a dynamical origin for the Lorentzian
signature is possible in the five-dimensional space with small torus radius (periodic boundary conditions), as well as in
four-dimensional space with trivial topology. Hence, the possibility exists
that the early universe might have been of the Kaluza-Klein type, \ie
multidimensional and of Lorentzian signature.Comment: 10 pages, LaTeX file, 4 figure
Signature change events: A challenge for quantum gravity?
Within the framework of either Euclidian (functional-integral) quantum
gravity or canonical general relativity the signature of the manifold is a
priori unconstrained. Furthermore, recent developments in the emergent
spacetime programme have led to a physically feasible implementation of
signature change events. This suggests that it is time to revisit the sometimes
controversial topic of signature change in general relativity. Specifically, we
shall focus on the behaviour of a quantum field subjected to a manifold
containing regions of different signature. We emphasise that, regardless of the
underlying classical theory, there are severe problems associated with any
quantum field theory residing on a signature-changing background. (Such as the
production of what is naively an infinite number of particles, with an infinite
energy density.) From the viewpoint of quantum gravity phenomenology, we
discuss possible consequences of an effective Lorentz symmetry breaking scale.
To more fully understand the physics of quantum fields exposed to finite
regions of Euclidean-signature (Riemannian) geometry, we show its similarities
with the quantum barrier penetration problem, and the super-Hubble horizon
modes encountered in cosmology. Finally we raise the question as to whether
signature change transitions could be fully understood and dynamically
generated within (modified) classical general relativity, or whether they
require the knowledge of a full theory of quantum gravity.Comment: 33 pages. 4 figures; V2: 3 references added, no physics changes; V3:
now 24 pages - significantly shortened - argument simplified and more focused
- no physics changes - this version accepted for publication in Classical and
Quantum Gravit
Comment on "Failure of standard conservation laws at a classical change of signature"
Hellaby & Dray (gr-qc/9404001) have recently claimed that matter conservation
fails under a change of signature, compounding earlier claims that the standard
junction conditions for signature change are unnecessary. In fact, if the field
equations are satisfied, then the junction conditions and the conservation
equations are satisfied. The failure is rather that the authors did not make
sense of the field equations and conservation equations, which are singular at
a change of signature.Comment: 3 pages, Te
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