Hidden gauge structure and derivation of microcanonical ensemble theory of bosons from quantum principles

Microcanonical ensemble theory of bosons is derived from quantum mechanics by making use of a hidden gauge structure. The relative phase interaction associated with this gauge structure, described by the Pegg-Barnett formalism, is shown to lead to perfect decoherence in the thermodynamics limit and the principle of equal a priori probability, simultaneously.Comment: 10 page

Local gauge theory and coarse graining

Within the discrete gauge theory which is the basis of spin foam models, the problem of macroscopically faithful coarse graining is studied. Macroscopic data is identified; it contains the holonomy evaluation along a discrete set of loops and the homotopy classes of certain maps. When two configurations share this data they are related by a local deformation. The interpretation is that such configurations differ by "microscopic details". In many cases the homotopy type of the relevant maps is trivial for every connection; two important cases in which the homotopy data is composed by a set of integer numbers are: (i) a two dimensional base manifold and structure group U(1), (ii) a four dimensional base manifold and structure group SU(2). These cases are relevant for spin foam models of two dimensional gravity and four dimensional gravity respectively. This result suggests that if spin foam models for two-dimensional and four-dimensional gravity are modified to include all the relevant macroscopic degrees of freedom -the complete collection of macroscopic variables necessary to ensure faithful coarse graining-, then they could provide appropriate effective theories at a given scale.Comment: Based on talk given at Loops 11-Madri

Global analysis by hidden symmetry

Hidden symmetry of a G'-space X is defined by an extension of the G'-action on X to that of a group G containing G' as a subgroup. In this setting, we study the relationship between the three objects: (A) global analysis on X by using representations of G (hidden symmetry); (B) global analysis on X by using representations of G'; (C) branching laws of representations of G when restricted to the subgroup G'. We explain a trick which transfers results for finite-dimensional representations in the compact setting to those for infinite-dimensional representations in the noncompact setting when $X_C$ is $G_C$-spherical. Applications to branching problems of unitary representations, and to spectral analysis on pseudo-Riemannian locally symmetric spaces are also discussed.Comment: Special volume in honor of Roger Howe on the occasion of his 70th birthda

Role of anion size, magnetic moment, and disorder on the properties of the organic conductor kappa-(BETS)_2Ga_{1-x}Fe_{x}Cl_{4-y}_Br_{y}

Shubnikov-de Haas and angular dependent magnetoresistance oscillations have been used to explore the role of anion size, magnetic moment, and disorder in the organic conductors kappa-(BETS)_2GaBr_{4} and kappa-(BETS)_2FeCl_{2}_Br_{2} in the isomorphic class kappa-(BETS)_2Ga_{1-x}Fe_{x}Cl_{4-y}_Br_{y}. The results, combined with previous work, show correlations between the anion composition (Ga_{1-x}Fe_{x}Cl_{4-y}_Br_{y}) and the superconducting transition temperature, effective mass, Fermi surface topology, and the mean free path.Comment: 5 pages, 6 figure

Co-NMR Knight Shift of NaxCoO2 \dot yH2O Studied in Both Superconducting Regions of the Tc-nuQ3 Phase Diagram Divided by the Nonsuperconducting Phase

In the temperature (T)-nuQ3 phase diagram of NaxCoO2 \dot yH2O, there exist two superconducting regions of nuQ3 separated by the nonsuperconducting region, where nuQ3 is usually estimated from the peak position of the 59Co-NQR spectra of the 5/2-7/2 transition and well-approximated here as nuQ3~3nuQ,nuQ being the interaction energy between the nuclear quadrupole moment and the electric field gradient. We have carried out measurements of the 59Co-NMR Knight shift (K) for a single crystal in the higher-nuQ3 superconducting phase and found that K begins to decrease with decreasing T at Tc for both magnetic field directions parallel and perpendicular to CoO2-planes. The result indicates together with the previous ones that the superconducting pairs are in the spin-singlet state in both phases, excluding the possibility of the spin-triplet superconductivity in this phase diagram. The superconductivity of this system spreads over the wide nuQ3 regions, but is suppressed in the narrow region located at the middle point of the region possibly due to charge instability.Comment: 8 pages, 5 figures, submitted to J. Phys. Soc. Jp

Two observers calculate the trace anomaly

We adapt a calculation due to Massacand and Schmid to the coordinate independent definition of time and vacuum given by Capri and Roy in order to compute the trace anomaly for a massless scalar field in a curved spacetime in 1+1 dimensions. The computation which requires only a simple regulator and normal ordering yields the well-known result $\frac{R}{24\pi}$ in a straightforward manner.Comment: RevTeX, 13 pages, some typos corrected and an appendix added, this is the version to appear in Class. and Quantum Gavit

Fermion spectrum and localization on kinks in a deconstructed dimension

We study the deconstructed scalar theory having nonlinear interactions and being renormalizable. It is shown that the kink-like configurations exist in such models. The possible forms of Yukawa coupling are considered. We find the degeneracy in mass spectrum of fermions coupled to the nontrivial scalar configuration.Comment: 19pages, 39figures, revised versio