26 research outputs found
Once again about quantum deformations of D=4 Lorentz algebra: twistings of q-deformation
This paper together with the previous one (arXiv:hep-th/0604146) presents the
detailed description of all quantum deformations of D=4 Lorentz algebra as Hopf
algebra in terms of complex and real generators. We describe here in detail two
quantum deformations of the D=4 Lorentz algebra o(3,1) obtained by twisting of
the standard q-deformation U_{q}(o(3,1)). For the first twisted q-deformation
an Abelian twist depending on Cartan generators of o(3,1) is used. The second
example of twisting provides a quantum deformation of Cremmer-Gervais type for
the Lorentz algebra. For completeness we describe also twisting of the Lorentz
algebra by standard Jordanian twist. By twist quantization techniques we obtain
for these deformations new explicit formulae for the deformed coproducts and
antipodes of the o(3,1)-generators.Comment: 17 page
Modern tests of Lorentz invariance
Motivated by ideas about quantum gravity, a tremendous amount of effort over
the past decade has gone into testing Lorentz invariance in various regimes.
This review summarizes both the theoretical frameworks for tests of Lorentz
invariance and experimental advances that have made new high precision tests
possible. The current constraints on Lorentz violating effects from both
terrestrial experiments and astrophysical observations are presented.Comment: Modified and expanded discussions of various points. Numerous
references added. Version matches that accepted by Living Reviews in
Relativit
New varying speed of light theories
We review recent work on the possibility of a varying speed of light (VSL).
We start by discussing the physical meaning of a varying , dispelling the
myth that the constancy of is a matter of logical consistency. We then
summarize the main VSL mechanisms proposed so far: hard breaking of Lorentz
invariance; bimetric theories (where the speeds of gravity and light are not
the same); locally Lorentz invariant VSL theories; theories exhibiting a color
dependent speed of light; varying induced by extra dimensions (e.g. in the
brane-world scenario); and field theories where VSL results from vacuum
polarization or CPT violation. We show how VSL scenarios may solve the
cosmological problems usually tackled by inflation, and also how they may
produce a scale-invariant spectrum of Gaussian fluctuations, capable of
explaining the WMAP data. We then review the connection between VSL and
theories of quantum gravity, showing how ``doubly special'' relativity has
emerged as a VSL effective model of quantum space-time, with observational
implications for ultra high energy cosmic rays and gamma ray bursts. Some
recent work on the physics of ``black'' holes and other compact objects in VSL
theories is also described, highlighting phenomena associated with spatial (as
opposed to temporal) variations in . Finally we describe the observational
status of the theory. The evidence is currently slim -- redshift dependence in
the atomic fine structure, anomalies with ultra high energy cosmic rays, and
(to a much lesser extent) the acceleration of the universe and the WMAP data.
The constraints (e.g. those arising from nucleosynthesis or geological bounds)
are tight, but not insurmountable. We conclude with the observational
predictions of the theory, and the prospects for its refutation or vindication.Comment: Final versio
Minimal Length Scale Scenarios for Quantum Gravity
We review the question of whether the fundamental laws of nature limit our
ability to probe arbitrarily short distances. First, we examine what insights
can be gained from thought experiments for probes of shortest distances, and
summarize what can be learned from different approaches to a theory of quantum
gravity. Then we discuss some models that have been developed to implement a
minimal length scale in quantum mechanics and quantum field theory. These
models have entered the literature as the generalized uncertainty principle or
the modified dispersion relation, and have allowed the study of the effects of
a minimal length scale in quantum mechanics, quantum electrodynamics,
thermodynamics, black-hole physics and cosmology. Finally, we touch upon the
question of ways to circumvent the manifestation of a minimal length scale in
short-distance physics.Comment: Published version available at
http://www.livingreviews.org/lrr-2013-
Quantum Spacetime Phenomenology
I review the current status of phenomenological programs inspired by
quantum-spacetime research. I stress in particular the significance of results
establishing that certain data analyses provide sensitivity to effects
introduced genuinely at the Planck scale. And my main focus is on
phenomenological programs that managed to affect the directions taken by
studies of quantum-spacetime theories.Comment: 125 pages, LaTex. This V2 is updated and more detailed than the V1,
particularly for quantum-spacetime phenomenology. The main text of this V2 is
about 25% more than the main text of the V1. Reference list roughly double