Simplifying the spectral analysis of the volume operator

The volume operator plays a central role in both the kinematics and dynamics of canonical approaches to quantum gravity which are based on algebras of generalized Wilson loops. We introduce a method for simplifying its spectral analysis, for quantum states that can be realized on a cubic three-dimensional lattice. This involves a decomposition of Hilbert space into sectors transforming according to the irreducible representations of a subgroup of the cubic group. As an application, we determine the complete spectrum for a class of states with six-valent intersections.Comment: 19 pages, TeX, to be published in Nucl. Phys.

Quantum groups, Yang-Baxter maps and quasi-determinants

For any quasi-triangular Hopf algebra, there exists the universal R-matrix, which satisfies the Yang-Baxter equation. It is known that the adjoint action of the universal R-matrix on the elements of the tensor square of the algebra constitutes a quantum Yang-Baxter map, which satisfies the set-theoretic Yang-Baxter equation. The map has a zero curvature representation among L-operators defined as images of the universal R-matrix. We find that the zero curvature representation can be solved by the Gauss decomposition of a product of L-operators. Thereby obtained a quasi-determinant expression of the quantum Yang-Baxter map associated with the quantum algebra $U_{q}(gl(n))$. Moreover, the map is identified with products of quasi-Pl\"{u}cker coordinates over a matrix composed of the L-operators. We also consider the quasi-classical limit, where the underlying quantum algebra reduces to a Poisson algebra. The quasi-determinant expression of the quantum Yang-Baxter map reduces to ratios of determinants, which give a new expression of a classical Yang-Baxter map.Comment: 46 page

The SUSY EW-like corrections to top pair production in photon-photon collisions

We studied the one-loop contributions of the gaugino-Higgsino-sector to the process of top-pair production via $\gamma \gamma$ fusion at NLC in frame of the Minimal Supersymmetric Model(MSSM). We find that the corrections to $\gamma \gamma \to t\bar{t}$ and $e^+ e^- \to \gamma \gamma \to t\bar{t}$ are found to be significant and can approach to a few percent and one percent, respectively. Furthermore, the dependences of the corrections on the supersymmetric parameters are also investigated. The corrections are not sensitive to $M_{SU(2)}$ (or $|\mu|$) when $M_{SU(2)}~>>~|\mu|$ (or $|\mu|~>>~M_{SU(2)}$) and are weakly dependent on the $\tan{\beta}$ with $M_Q$ (or $|\mu|$) being large enough. But they are sensitive to the c.m.s. energy of the incoming photons.Comment: LaTex, 33 pages, 8 Eps figuer

Discrete Nonholonomic LL Systems on Lie Groups

This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical nonholonomic systems, the Suslov top and the Chaplygin sleigh. The preservation of the reduced energy by the discrete flow is observed and the discrete momentum conservation is discussed.Comment: 32 pages, 13 figure

Lepton-flavour violating decays in theories with dimension 6 operators

Despite a large experimental effort, so far no evidence for flavour-violating decays of charged leptons such as $l_i\to l_j\gamma$ and $l_i\to l_j l_k l_k$ has been found. The absence of a signal puts very severe constraints on many extensions of the Standard Model. Here we apply a model independent approach by studying such decays in the Standard Model effective field theory. Going beyond leading order in the Standard Model couplings and considering all dimension 6 operators that might lead to lepton-flavour violation, we are able to extract limits on a large number of Wilson coefficients of such operators. We are also able to compare the impact of particular searches and find, for example, that flavour-violating decays of the $Z$-boson $Z\to \mu e$ are much more constrained from low-energy experiments $\mu\to e \gamma$ than from the limits of current and future direct searches at high energy.Comment: 7 pages, 5 Tables; to appear in the Proceedings of the FCCP2015 Worksho

Nonhomogeneous distributions and optimal quantizers for Sierpi\'nski carpets

The purpose of quantization of a probability distribution is to estimate the probability by a discrete probability with finite support. In this paper, a nonhomogeneous probability measure $P$ on $\mathbb R^2$ which has support the Sierpi\'nski carpet generated by a set of four contractive similarity mappings with equal similarity ratios has been considered . For this probability measure, the optimal sets of $n$-means and the $n$th quantization errors are investigated for all $n\geq 2$.Comment: arXiv admin note: text overlap with arXiv:1603.0073

Dynamically Generated Open and Hidden Charm Meson Systems

We will study open and hidden charm scalar meson resonances within two different models. The first one is a direct application of a chiral Lagrangian already used to study flavor symmetry breaking in Skyrme models. In another approach to the problem a SU(4) symmetric Lagrangian is built and the symmetry is broken down to SU(3) by identifying currents where heavy mesons are exchanged and suppressing those. Unitarization in couple channels leads to dynamical generation of resonances in both models, in particular a new hidden charm resonance with mass 3.7 GeV is predicted. The small differences between these models and with previous works will be discussed.Comment: 32 pages, 10 figures. Added extra calculations with explicit symmetry breaking terms in chiral Lagrangian