Extended Loop Quantum Gravity

We discuss constraint structure of extended theories of gravitation (also known as f(R) theories) in the vacuum selfdual formulation introduced in ref. [1].Comment: 7 pages, few typos correcte

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

Constraints on the quantum gravity scale from kappa - Minkowski spacetime

We compare two versions of deformed dispersion relations (energy vs momenta and momenta vs energy) and the corresponding time delay up to the second order accuracy in the quantum gravity scale (deformation parameter). A general framework describing modified dispersion relations and time delay with respect to different noncommutative kappa -Minkowski spacetime realizations is firstly proposed here and it covers all the cases introduced in the literature. It is shown that some of the realizations provide certain bounds on quadratic corrections, i.e. on quantum gravity scale, but it is not excluded in our framework that quantum gravity scale is the Planck scale. We also show how the coefficients in the dispersion relations can be obtained through a multiparameter fit of the gamma ray burst (GRB) data.Comment: 9 pages, final published version, revised abstract, introduction and conclusion, to make it clear to general reade

Noether's second theorem in a general setting. Reducible gauge theories

We prove Noether's direct and inverse second theorems for Lagrangian systems on fiber bundles in the case of gauge symmetries depending on derivatives of dynamic variables of an arbitrary order. The appropriate notions of reducible gauge symmetries and Noether's identities are formulated, and their equivalence by means of certain intertwining operator is proved.Comment: 20 pages, to be published in J. Phys. A (2005

The LHC Beam Pipe Waveguide Mode Reflectometer

The waveguide-mode reflectometer for obstacle detection in the LHC beam pipe has been intensively used for more than 18 months. The âﾜAssemblyâ version is based on the synthetic pulse method using a modern vector network analyzer. It has mode selective excitation couplers for the first TE and TM mode and uses a specially developed waveguide mode dispersion compensation algorithm with external software. In addition there is a similar âﾜIn Situâ version of the reflectometer which uses permanently installed microwave couplers at the end of each of the nearly 3 km long LHC arcs. During installation a considerable number of unexpected objects have been found in the beam pipes and subsequently removed. Operational statistics and lessons learned are presented and the overall performance is discussed

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