On the Decoupling of the Homogeneous and Inhomogeneous Parts in Inhomogeneous Quantum Groups

We show that, if there exists a realization of a Hopf algebra $H$ in a $H$-module algebra $A$, then one can split their cross-product into the tensor product algebra of $A$ itself with a subalgebra isomorphic to $H$ and commuting with $A$. This result applies in particular to the algebra underlying inhomogeneous quantum groups like the Euclidean ones, which are obtained as cross-products of the quantum Euclidean spaces $R_q^N$ with the quantum groups of rotation $U_qso(N)$ of $R_q^N$, for which it has no classical analog.Comment: Latex file, 27 pages. Final version to appear in J. Phys.

Unbraiding the braided tensor product

We show that the braided tensor product algebra $A_1\underline{\otimes}A_2$ of two module algebras $A_1, A_2$ of a quasitriangular Hopf algebra $H$ is equal to the ordinary tensor product algebra of $A_1$ with a subalgebra of $A_1\underline{\otimes}A_2$ isomorphic to $A_2$, provided there exists a realization of $H$ within $A_1$. In other words, under this assumption we construct a transformation of generators which `decouples' $A_1, A_2$ (i.e. makes them commuting). We apply the theorem to the braided tensor product algebras of two or more quantum group covariant quantum spaces, deformed Heisenberg algebras and q-deformed fuzzy spheres.Comment: LaTex file, 29 page

Nuclear higher-twist effects in eA DIS

We discuss the relation between the treatments of the higher twist nuclear effects in eA DIS based on the pQCD collinear approximation and the light-cone path integral formalism. We show that in the collinear approximation the N=1 rescattering contribution to the gluon emission vanishes. It is demonstrated that the nonzero gluon spectrum obtained by Guo, Wang and Zhang is a consequence of unjustified neglect of some terms in the collinear expansion.Comment: Talk given at Diffraction 2008: International Workshop on Diffraction in High Energy Physics, La Londe-les-Maures, France, 9-14 Sep 200

Frame formalism for the N-dimensional quantum Euclidean spaces

We sketch our recent application of a non-commutative version of the Cartan `moving-frame' formalism to the quantum Euclidean space $R^N_q$, the space which is covariant under the action of the quantum group $SO_q(N)$. For each of the two covariant differential calculi over $R^N_q$ based on the $R$-matrix formalism, we summarize our construction of a frame, the dual inner derivations, a metric and two torsion-free almost metric compatible covariant derivatives with a vanishing curvature. To obtain these results we have developed a technique which fully exploits the quantum group covariance of $R^N_q$. We first find a frame in the larger algebra \Omega^*(R^N_q) \cocross \uqs. Then we define homomorphisms from R^N_q \cocross U_q^{\pm}{so(N)} to $R^N_q$ which we use to project this frame in $\Omega^*(R^N_q)$.Comment: Latex file, 11 pages. Talks given at the Euroconference ``Non-commutative Geometry and Hopf Algebras in Field Theory and Particle Physics'', Villa Gualino (Torino), Sept. 199

On Quantum Groups in the Hubbard Model with Phonons

The correct Hamiltonian for an extended Hubbard model with quantum group symmetry as introduced by A. Montorsi and M. Rasetti is derived for a D-dimensional lattice. It is shown that the superconducting SUq(2) holds as a true quantum symmetry only for D = 1 and that terms of higher order in the fermionic operators in addition to phonons are required for a quantum symmetric hamiltonian. The condition for quantum symmetry is "half filling" and there is no local electron-phonon coupling. A discussion of Quantum symmetries in general is given in a formalism that should be readily accessible to non Hopf-algebraists.Comment: latex, 17 page

Single photonics at telecom wavelengths using nanowire superconducting detectors

Single photonic applications - such as quantum key distribution - rely on the transmission of single photons, and require the ultimate sensitivity that an optical detector can achieve. Single-photon detectors must convert the energy of an optical pulse containing a single photon into a measurable electrical signal. We report on fiber-coupled superconducting single-photon detectors (SSPDs) with specifications that exceed those of avalanche photodiodes (APDs), operating at telecommunication wavelength, in sensitivity, temporal resolution and repetition frequency. The improved performance is demonstrated by measuring the intensity correlation function g(2)(t) of single-photon states at 1300nm produced by single semiconductor quantum dots (QDs).Comment: 7 pages, 5 figures - submitted 12 OCT 200

Effect of strong magnetic field on the first-order electroweak phase transition

The broken-symmetry electroweak vacuum is destabilized in the presence of a magnetic field stronger than a critical value. Such magnetic field may be generated in the phase transition and restore the symmetry inside the bubbles. A numerical calculation indicates that the first-order phase transition is delayed but may be completed for a sufficient low value of the Higgs mass unless the magnetic field is extremely high.Comment: 7 pages including 2 figures, uses epsf.sty; discussion regarding cosmological consequences (e.g. on baryogenesis) enlarged, some references added and a few misprints correcte