8 research outputs found
Non-Commutative Geometry and Chiral Perturbation Lagrangian
Chiral perturbation lagrangian in the framework of non-commutative geometry
is considered in full detail. It is found that the explicit symmetry breaking
terms appear and some relations between the coupling constants of the theory
come out naturally. The WZW term also turns up on the same footing as the other
terms of the chiral lagrangian.Comment: Latex, 9 page
Star Product and Invariant Integration for Lie type Noncommutative Spacetimes
We present a star product for noncommutative spaces of Lie type, including
the so called ``canonical'' case by introducing a central generator, which is
compatible with translations and admits a simple, manageable definition of an
invariant integral. A quasi-cyclicity property for the latter is shown to hold,
which reduces to exact cyclicity when the adjoint representation of the
underlying Lie algebra is traceless. Several explicit examples illuminate the
formalism, dealing with kappa-Minkowski spacetime and the Heisenberg algebra
(``canonical'' noncommutative 2-plane).Comment: 21 page
Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
We derive noncommutative Einstein equations for abelian twists and their
solutions in consistently symmetry reduced sectors, corresponding to twisted
FRW cosmology and Schwarzschild black holes. While some of these solutions must
be rejected as models for physical spacetimes because they contradict
observations, we find also solutions that can be made compatible with low
energy phenomenology, while exhibiting strong noncommutativity at very short
distances and early times.Comment: LaTeX 12 pages, JHEP.st
Emission and absorption of photons and the black-body spectra in Lorentz-odd Electrodynamics
We study a number of issues related to the emission and absorption radiation
by non-relativistic electrons within the framework of a Lorentz-breaking
electrodynamics in (3+1) dimensions. Our main results concern how Planck-like
spectrum law is sensitive to terms that violate Lorentz symmetry. We have
realized that Planck law acquires extra terms proportional to the violating
parameters: for the CPT-odd model, the leading extra terms appear to be linear
or quadratic in these violating parameters according to the background vector
is parallel or perpendicular to the photon wave-vector. In the CPT-even case a
linear `correction' shows up. Among other possible ways to probe for these
violations, by means of the present results, we may quote the direct
observation of the extra contributions or an unbalancing in the mean occupation
number of photon modes in a given thermal bath.Comment: 11 pages, Late
Quantum mechanics on space with SU(2) fuzziness
Quantum mechanics of models is considered which are constructed in spaces
with Lie algebra type commutation relations between spatial coordinates. The
case is specialized to that of the group SU(2), for which the formulation of
the problem via the Euler parameterization is also presented. SU(2)-invariant
systems are discussed, and the corresponding eigenvalue problem for the
Hamiltonian is reduced to an ordinary differential equation, as it is the case
with such models on commutative spaces.Comment: 12 pages, no figs, LaTe
Direction-Dependent CMB Power Spectrum and Statistical Anisotropy from Noncommutative Geometry
Modern cosmology has now emerged as a testing ground for theories beyond the
standard model of particle physics. In this paper, we consider quantum
fluctuations of the inflaton scalar field on certain noncommutative spacetimes
and look for noncommutative corrections in the cosmic microwave background
(CMB) radiation. Inhomogeneities in the distribution of large scale structure
and anisotropies in the CMB radiation can carry traces of noncommutativity of
the early universe. We show that its power spectrum becomes direction-dependent
when spacetime is noncommutative. (The effects due to noncommutativity can be
observed experimentally in the distribution of large scale structure of matter
as well.) Furthermore, we have shown that the probability distribution
determining the temperature fluctuations is not Gaussian for our noncommutative
spacetimes.Comment: 26 pages. v3: Minor correction