Algebraic characterization of constraints and generation of mass in gauge theories

The possibility of non-trivial representations of the gauge group on wavefunctionals of a gauge invariant quantum field theory leads to a generation of mass for intermediate vector and tensor bosons. The mass parameters "m" show up as central charges in the algebra of constraints, which then become of second-class nature. The gauge group coordinates acquire dynamics outside the null-mass shell and provide the longitudinal field degrees of freedom that massless bosons need to form massive bosons.Comment: 4 pages, LaTeX, no figures; uses espcrc2.sty (twocolumn). Contribution to the "Third Meeting on Constrained Dynamics and Quantum Gravity QG99" held in Sardinia, Italy, on Sept. 1999. To appear in Nucl. Phys. B (Proc. Suppl.

Gauge Transformation Properties of Vector and Tensor Potentials Revisited: a Group Quantization Approach

The possibility of non-trivial representations of the gauge group on wavefunctionals of a gauge invariant quantum field theory leads to a generation of mass for intermediate vector and tensor bosons. The mass parameters m show up as central charges in the algebra of constraints, which then become of second-class nature. The gauge group coordinates acquire dynamics outside the null-mass shell and provide the longitudinal field degrees of freedom that massless bosons need to form massive bosons. This is a `non-Higgs' mechanism that could provide new clues for the best understanding of the symmetry breaking mechanism in unified field theories. A unified quantization of massless and massive non-Abelian Yang-Mills, linear Gravity and Abelian two-form gauge field theories are fully developed from this new approach, where a cohomological origin of mass is pointed out.Comment: 22 pages, LaTeX, no figures; final version to appear in Int. J. Mod. Phys.

Wavelet Transform on the Circle and the Real Line: A Unified Group-Theoretical Treatment

We present a unified group-theoretical derivation of the Continuous Wavelet Transform (CWT) on the circle $\mathbb S^1$ and the real line $\mathbb{R}$, following the general formalism of Coherent States (CS) associated to unitary square integrable (modulo a subgroup, possibly) representations of the group $SL(2,\mathbb{R})$. A general procedure for obtaining unitary representations of a group $G$ of affine transformations on a space of signals $L^2(X,dx)$ is described, relating carrier spaces $X$ to (first or higher-order) ``polarization subalgebras'' ${\cal P}_X$. We also provide explicit admissibility and continuous frame conditions for wavelets on $\mathbb S^1$ and discuss the Euclidean limit in terms of group contraction.Comment: 32 pages, LaTeX, 1 figure. Final version published in ACH

Identifying topological-band insulator transitions in silicene and other 2D gapped Dirac materials by means of R\'enyi-Wehrl entropy

We propose a new method to identify transitions from a topological insulator to a band insulator in silicene (the silicon equivalent of graphene) in the presence of perpendicular magnetic and electric fields, by using the R\'enyi-Wehrl entropy of the quantum state in phase space. Electron-hole entropies display an inversion/crossing behavior at the charge neutrality point for any Landau level, and the combined entropy of particles plus holes turns out to be maximum at this critical point. The result is interpreted in terms of delocalization of the quantum state in phase space. The entropic description presented in this work will be valid in general 2D gapped Dirac materials, with a strong intrinsic spin-orbit interaction, isoestructural with silicene.Comment: to appear in EP

Husimi function and phase-space analysis of bilayer quantum Hall systems at ν=2/λ\nu=2/\lambda

We propose localization measures in phase space of the ground state of bilayer quantum Hall (BLQH) systems at fractional filling factors $\nu=2/\lambda$, to characterize the three quantum phases (shortly denoted by spin, canted and ppin) for arbitrary $U(4)$-isospin $\lambda$. We use a coherent state (Bargmann) representation of quantum states, as holomorphic functions in the 8-dimensional Grassmannian phase-space $\mathbb{G}^4_{2}=U(4)/[U(2)\times U(2)]$ (a higher-dimensional generalization of the Haldane's 2-dimensional sphere $\mathbb{S}^2=U(2)/[U(1)\times U(1)]$). We quantify the localization (inverse volume) of the ground state wave function in phase-space throughout the phase diagram (i.e., as a function of Zeeman, tunneling, layer distance, etc, control parameters) with the Husimi function second moment, a kind of inverse participation ratio that behaves as an order parameter. Then we visualize the different ground state structure in phase space of the three quantum phases, the canted phase displaying a much higher delocalization (a Schr\"odinger cat structure) than the spin and ppin phases, where the ground state is highly coherent. We find a good agreement between analytic (variational) and numeric diagonalization results.Comment: 13 pages, 6 figures. New section added. Novel results and insights further highlighte