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