3,169 research outputs found

### Low energy bounds on Poincare violation in causal set theory

In the causal set approach to quantum gravity, Poincar\'{e} symmetry is
modified by swerving in spacetime, induced by the random lattice discretization
of the space-time structure. The broken translational symmetry at short
distances is argued to lead to a residual diffusion in momentum space, whereby
a particle can acquire energy and momentum by drift along its mass shell and a
system in equilibrium can spontaneously heat up. We consider bounds on the rate
of momentum space diffusion coming from astrophysical molecular clouds, nuclear
stability and cosmological neutrino background. We find that the strongest
limits come from relic neutrinos, which we estimate to constrain the momentum
space diffusion constant by $k < 10^{-61} {\rm GeV}^3$ for neutrinos with
masses $m_\nu > 0.01 {\rm eV}$, improving the previously quoted bounds by
roughly 17 orders of magnitude.Comment: Additional discussion about behavior of alpha particles in nuclei
added. Version matches that accepted in PR

### Causal sets and conservation laws in tests of Lorentz symmetry

Many of the most important astrophysical tests of Lorentz symmetry also
assume that energy-momentum of the observed particles is exactly conserved. In
the causal set approach to quantum gravity a particular kind of Lorentz
symmetry holds but energy-momentum conservation may be violated. We show that
incorrectly assuming exact conservation can give rise to a spurious signal of
Lorentz symmetry violation for a causal set. However, the size of this spurious
signal is much smaller than can be currently detected and hence astrophysical
Lorentz symmetry tests as currently performed are safe from causal set induced
violations of energy-momentum conservation.Comment: 8 pages, matches version published in PR

### Einstein-Aether Waves

Local Lorentz invariance violation can be realized by introducing extra
tensor fields in the action that couple to matter. If the Lorentz violation is
rotationally invariant in some frame, then it is characterized by an
``aether'', i.e. a unit timelike vector field. General covariance requires that
the aether field be dynamical. In this paper we study the linearized theory of
such an aether coupled to gravity and find the speeds and polarizations of all
the wave modes in terms of the four constants appearing in the most general
action at second order in derivatives. We find that in addition to the usual
two transverse traceless metric modes, there are three coupled aether-metric
modes.Comment: 5 pages; v2: Remarks added concerning gauge invariance of the waves
and hyperbolicity of the equations. Essentially the version published in PR

### Renormalization of Scalar and Yukawa Field Theories with Lorentz Violation

We consider a theory of scalar and spinor fields, interacting through Yukawa
and phi^4 interactions, with Lorentz-violating operators included in the
Lagrangian. We compute the leading quantum corrections in this theory. The
renormalizability of the theory is explicitly shown up to one-loop order. In
the pure scalar sector, the calculations can be generalized to higher orders
and to include finite terms, because the theory can be solved in terms of its
Lorentz-invariant version.Comment: 30 page

### Threshold effects and Planck scale Lorentz violation: combined constraints from high energy astrophysics

Recent work has shown that dispersion relations with Planck scale Lorentz
violation can produce observable effects at energies many orders of magnitude
below the Planck energy M. This opens a window on physics that may reveal
quantum gravity phenomena. It has already constrained the possibility of Planck
scale Lorentz violation, which is suggested by some approaches to quantum
gravity. In this work we carry out a systematic analysis of reaction
thresholds, allowing unequal deformation parameters for different particle
dispersion relations. The thresholds are found to have some unusual properties
compared with standard ones, such as asymmetric momenta for pair creation and
upper thresholds. The results are used together with high energy observational
data to determine combined constraints. We focus on the case of photons and
electrons, using vacuum Cerenkov, photon decay, and photon annihilation
processes to determine order unity constraints on the parameters controlling
O(E/M) Lorentz violation. Interesting constraints for protons (with photons or
pions) are obtained even at O((E/M)^2), using the absence of vacuum Cerenkov
and the observed GZK cutoff for ultra high energy cosmic rays. A strong
Cerenkov limit using atmospheric PeV neutrinos is possible for O(E/M)
deformations provided the rate is high enough. If detected, ultra high energy
cosmological neutrinos might yield limits at or even beyond O((E/M)^2).Comment: 35 pages, 13 Figures, RevTex4. Version published in PRD. Expanded
introduction, updated discussion of possible constraint if GZK cutoff is
confirmed. Corrected typos. Added and updated reference

### High energy constraints on Lorentz symmetry violations

Lorentz violation at high energies might lead to non linear dispersion
relations for the fundamental particles. We analyze observational constraints
on these without assuming any a priori equality between the coefficients
determining the amount of Lorentz violation for different particle species. We
focus on constraints from three high energy processes involving photons and
electrons: photon decay, photo-production of electron-positron pairs, and
vacuum Cerenkov radiation. We find that cubic momentum terms in the dispersion
relations are strongly constrained.Comment: 7 pages, 1 figure, Talk presented at CPT01; the Second Meeting on CPT
and Lorentz Symmetry, Bloomington, Indiana, 15-18 Aug. 2001. Minor numerical
error corrected, gamma-decay constraint update

### Bounds on Spin-Dependent Lorentz Violation From Inverse Compton Observations

Some of the best bounds on possible Lorentz violation in the electron sector
come from observations of high-energy astrophysical phenomena. Using
measurements of TeV inverse Compton radiation from a number of sources, we
place the first bounds--at the 10^(-15) level--on seven of the electron d
coefficients.Comment: 10 page

### Radiatively Induced Lorentz and Gauge Symmetry Violation in Electrodynamics with Varying alpha

A time-varying fine structure constant alpha(t) could give rise to Lorentz-
and CPT-violating changes to the vacuum polarization, which would affect photon
propagation. Such changes to the effective action can violate gauge invariance,
but they are otherwise permitted. However, in the minimal theory of varying
alpha, no such terms are generated at lowest order. At second order, vacuum
polarization can generate an instability--a Lorentz-violating analogue of a
negative photon mass squared -m^2 proportional to alpha [(d alpha/dt) /
alpha]^2 log (Lambda^2), where Lambda is the cutoff for the low-energy
effective theory.Comment: 14 page

### On calculation of cross sections in Lorentz violating theories

We develop a systematic approach to the calculation of scattering cross
sections in theories with violation of the Lorentz invariance taking into
account the whole information about the theory Lagrangian. As an illustration
we derive the Feynman rules and formulas for sums over polarizations in spinor
electrodynamics with Lorentz violating operators of dimensions four and six.
These rules are applied to compute the probabilities of several astrophysically
relevant processes. We calculate the rates of photon decay and vacuum Cherenkov
radiation along with the cross sections of electron-positron pair production on
background radiation and in the Coulomb field. The latter process is essential
for detection of photon-induced air showers in the atmosphere.Comment: 23 pages, 1 figur

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