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

1/R multidimensional gravity with form-fields: stabilization of extra dimensions, cosmic acceleration and domain walls

We study multidimensional gravitational models with scalar curvature nonlinearity of the type 1/R and with form-fields (fluxes) as a matter source. It is assumed that the higher dimensional space-time undergoes Freund-Rubin-like spontaneous compactification to a warped product manifold. It is shown that for certain parameter regions the model allows for a freezing stabilization of the internal space near the positive minimum of the effective potential which plays the role of the positive cosmological constant. This cosmological constant provides the observable late-time accelerating expansion of the Universe if parameters of the model is fine tuned. Additionally, the effective potential has the saddle point. It results in domain walls in the Universe. We show that these domain walls do not undergo inflation.Comment: 10 pages, revtex, 5 eps figures, footnotes and references adde

A double-sum Kronecker-type identity

We prove a double-sum analog of an identity known to Kronecker and then express it in terms of functions studied by Appell and Kronecker's student Lerch, in so doing we show that the double-sum analog is of mixed mock modular form. We also give related symmetric generalizations.Comment: Major revisions. Identities (1.10) and (1.11) are ne

Gauge Theories with Cayley-Klein SO(2;j)SO(2;j) and SO(3;j)SO(3;j) Gauge Groups

Gauge theories with the orthogonal Cayley-Klein gauge groups $SO(2;j)$ and $SO(3;{\bf j})$ are regarded. For nilpotent values of the contraction parameters ${\bf j}$ these groups are isomorphic to the non-semisimple Euclid, Newton, Galilei groups and corresponding matter spaces are fiber spaces with degenerate metrics. It is shown that the contracted gauge field theories describe the same set of fields and particle mass as $SO(2), SO(3)$ gauge theories, if Lagrangians in the base and in the fibers all are taken into account. Such theories based on non-semisimple contracted group provide more simple field interactions as compared with the initial ones.Comment: 14 pages, 5 figure

Simultaneous maximum-likelihood calibration of odometry and sensor parameters

For a differential-drive mobile robot equipped with an on-board range sensor, there are six parameters to calibrate: three for the odometry (radii and distance between the wheels), and three for the pose of the sensor with respect to the robot frame. This paper describes a method for calibrating all six parameters at the same time, without the need for external sensors or devices. Moreover, it is not necessary to drive the robot along particular trajectories. The available data are the measures of the angular velocities of the wheels and the range sensor readings. The maximum-likelihood calibration solution is found in a closed form

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

Macroscopic limit of a bipartite Curie-Weiss model: a dynamical approach

We analyze the Glauber dynamics for a bi-populated Curie-Weiss model. We obtain the limiting behavior of the empirical averages in the limit of infinitely many particles. We then characterize the phase space of the model in absence of magnetic field and we show that several phase transitions in the inter-groups interaction strength occur.Comment: 18 pages, 3 figure