2,324 research outputs found
Interferometers as Probes of Planckian Quantum Geometry
A theory of position of massive bodies is proposed that results in an
observable quantum behavior of geometry at the Planck scale, . Departures
from classical world lines in flat spacetime are described by Planckian
noncommuting operators for position in different directions, as defined by
interactions with null waves. The resulting evolution of position wavefunctions
in two dimensions displays a new kind of directionally-coherent quantum noise
of transverse position. The amplitude of the effect in physical units is
predicted with no parameters, by equating the number of degrees of freedom of
position wavefunctions on a 2D spacelike surface with the entropy density of a
black hole event horizon of the same area. In a region of size , the effect
resembles spatially and directionally coherent random transverse shear
deformations on timescale with typical amplitude . This quantum-geometrical "holographic noise" in position is not
describable as fluctuations of a quantized metric, or as any kind of
fluctuation, dispersion or propagation effect in quantum fields. In a Michelson
interferometer the effect appears as noise that resembles a random Planckian
walk of the beamsplitter for durations up to the light crossing time. Signal
spectra and correlation functions in interferometers are derived, and predicted
to be comparable with the sensitivities of current and planned experiments. It
is proposed that nearly co-located Michelson interferometers of laboratory
scale, cross-correlated at high frequency, can test the Planckian noise
prediction with current technology.Comment: 23 pages, 6 figures, Latex. To appear in Physical Review
The Theory of a Quantum Noncanonical Field in Curved Spacetimes
Much attention has been recently devoted to the possibility that quantum
gravity effects could lead to departures from Special Relativity in the form of
a deformed Poincar\`e algebra. These proposals go generically under the name of
Doubly or Deformed Special Relativity (DSR). In this article we further explore
a recently proposed class of quantum field theories, involving noncanonically
commuting complex scalar fields, which have been shown to entail a DSR-like
symmetry. An open issue for such theories is whether the DSR-like symmetry has
to be taken as a physically relevant symmetry, or if in fact the "true"
symmetries of the theory are just rotations and translations while boost
invariance has to be considered broken. We analyze here this issue by extending
the known results to curved spacetime under both of the previous assumptions.
We show that if the symmetry of the free theory is taken to be a DSR-like
realization of the Poincar\'e symmetry, then it is not possible to render such
a symmetry a gauge symmetry of the curved physical spacetime. However, it is
possible to introduce an auxiliary spacetime which allows to describe the
theory as a standard quantum field theory in curved spacetime. Alternatively,
taking the point of view that the noncanonical commutation of the fields
actually implies a breakdown of boost invariance, the physical spacetime
manifold has to be foliated in surfaces of simultaneity and the field theory
can be coupled to gravity by making use of the ADM prescription.Comment: 9 pages, no figure
Non-local on-shell field redefinition for the SME
This work instigates a study of non-local field mappings within the Lorentz-
and CPT-violating Standard-Model Extension (SME). An example of such a mapping
is constructed explicitly, and the conditions for the existence of its inverse
are investigated. It is demonstrated that the associated field redefinition can
remove b-type Lorentz violation from free SME fermions in certain situations.
These results are employed to obtain explicit expressions for the corresponding
Lorentz-breaking momentum-space eigenspinors and their orthogonality relations.Comment: 12 pages, REVTeX
Synchrotron Radiation in the Standard Model Extension
We obtain a system of exact solutions of the Dirac equation for an electron
moving in a constant homogeneous external magnetic field with account of its
vacuum magnetic moment and assumed Lorentz invariance violation in the minimal
CPT-odd form in the framework of the Standard Model Extension. Using these
solutions, characteristics of the particle synchrotron radiation are
calculated, and possible observable effects caused by the Lorentz non-invariant
interaction are described. We demonstrate that the angular distribution of the
radiation has specific asymmetry, which can be explained as a consequence of
non-conservation of transversal electron polarization in the presence of a
background Lorentz non-invariant condensate field.Comment: 14 pages, 2 figure
Modified dispersion relations and the response of the rotating Unruh-DeWitt detector
We study the response of a rotating monopole detector that is coupled to a
massless scalar field which is described by a non-linear dispersion relation in
flat spacetime. Since it does not seem to be possible to evaluate the response
of the rotating detector analytically, we resort to numerical computations.
Interestingly, unlike the case of the uniformly accelerated detector that has
been considered recently, we find that defining the transition probability rate
of the rotating detector poses no difficulties. Further, we show that the
response of the rotating detector can be computed {\it exactly}\vee (albeit,
numerically) even when it is coupled to a field that is governed by a
non-linear dispersion relation. We also discuss the response of the rotating
detector in the presence of a cylindrical boundary on which the scalar field is
constrained to vanish. While super-luminal dispersion relations hardly affect
the standard results, we find that sub-luminal dispersion relations can lead to
relatively large modifications.Comment: V1: 11 pages, 3 figures; V2: 12 pages, 3 figures, considerably
revised, we now calculate the detector response exactly; V3: 14 pages, 3
figures, minor changes, to appear in Phys. Rev.
The Casimir Force in a Lorentz Violating Theory
We study the effects of the minimal extension of the standard model including
Lorentz violation on the Casimir force between two parallel conducting plates
in vacuum. We provide explicit solutions for the electromagnetic field using
scalar field analogy, for both the cases in which the Lorentz violating terms
come from the CPT-even or CPT-odd terms. We also calculate the effects of the
Lorentz violating terms for a fermion field between two parallel conducting
plates and analyze the modifications of the Casimir force due to the
modifications of the Dirac equation. In all cases under consideration, the
standard formulas for the Casimir force are modified by either multiplicative
or additive correction factors, the latter case exhibiting different dependence
on the distance between the plates.Comment: 20 pages, no figures, references added, accepted for publication in
Phys. Rev.
Lorentz-symmetry violating decays in a medium
Various decay processes, such as the decay of a spin-1 particle into two
photons or the gravitational decay of a spin-1/2 fermion, are forbidden in the
vacuum by a combination of requirements, including angular momentum
conservation, Lorentz invariance and gauge invariance. We show that such
processes can occur in a medium, such as a thermal background of particles,
even if it is homogeneous and isotropic. We carry out a model-independent
analysis of the vertex function for such processes in terms of a set of form
factors, and show that the amplitude can be non-zero while remaining consistent
with the symmetry principles mentioned above. The results simulate Lorentz
symmetry violating effects, although in this case they arise from completely
Lorentz-invariant physics.Comment: 16 pages, Latex, no figure
Bounds on Lorentz and CPT Violation from the Earth-Ionosphere Cavity
Electromagnetic resonant cavities form the basis of many tests of Lorentz
invariance involving photons. The effects of some forms of Lorentz violation
scale with cavity size. We investigate possible signals of violations in the
naturally occurring resonances formed in the Earth-ionosphere cavity.
Comparison with observed resonances places the first terrestrial constraints on
coefficients associated with dimension-three Lorentz-violating operators at the
level of 10^{-20} GeV.Comment: 8 pages REVTe
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