Quantum Mechanical Breaking of Local GL(4) Invariance

We consider the gravitational coupling of a scalar field, in a reformulation of General Relativity exhibiting local GL(4) invariance at the classical level. We compute the one-loop contribution of the scalar to the quantum effective potential of the vierbein and find that it does not have GL(4) invariance. The minima of the effective potential occur for a vierbein which is proportional to the unit matrix.Comment: 9 pages, plain-TeX, no figure

On the use of Mellin transform to a class of q-difference-differential equations

We explore the possibility of using the method of classical integral transforms to solve a class of $q$-difference-differential equations. The Laplace and the Mellin transform of $q$-derivatives are derived. The results show that the Mellin transform of the $q$-derivative resembles most closely the corresponding expression in classical analysis, and it could therefore be useful in solving certain $q$-difference equations.Comment: 13 pages, LaTex, no figure

A model for the continuous q-ultraspherical polynomials

We provide an algebraic interpretation for two classes of continuous $q$-polynomials. Rogers' continuous $q$-Hermite polynomials and continuous $q$-ultraspherical polynomials are shown to realize, respectively, bases for representation spaces of the $q$-Heisenberg algebra and a $q$-deformation of the Euclidean algebra in these dimensions. A generating function for the continuous $q$-Hermite polynomials and a $q$-analog of the Fourier-Gegenbauer expansion are naturally obtained from these models

Tests of Complete Positivity in Fiber Optics

We consider the propagation of polarized photons in optical fibers under the action of randomly generated noise. In such situation, the change in time of the photon polarization can be described by a quantum dynamical semigroup. We show that the hierarchy among the decay constants of the polarization density matrix elements as prescribed by complete positivity can be experimentally probed using standard laboratory set-ups.Comment: 10 pages, LaTe

Open system approach to neutrino oscillations

Neutrino oscillations are studied in the general framework of open quantum systems by means of extended dynamics that take into account possible dissipative effects. These new phenomena induce modifications in the neutrino oscillation pattern that in general can be parametrized by means of six phenomenological constants. Although very small, stringent bounds on these parameters are likely to be given by future planned neutrino experiments.Comment: 15 pages, plain-TeX, to appear in JHE

Complete positivity and neutron interferometry

We analyze the dynamics of neutron beams in interferometry experiments using quantum dynamical semigroups. We show that these experiments could provide stringent limits on the non-standard, dissipative terms appearing in the extended evolution equations.Comment: 12 pages, plain Te

Direct CP-violation as a test of quantum mechanics

Direct CP-violating effects in the neutral kaon system result in violations of certain Bell-like inequalities. The new experimental results on the determination of the phenomenological parameter epsilon' allow to dismiss a large class of ``hidden variable'' alternatives to quantum mechanics.Comment: 15 pages, Te

Massless neutrino oscillations

Quantum dynamical semigroups provide a general framework for studying the evolution of open systems. Neutrino propagation both in vacuum and in matter can be analyzed using these techniques: they allow a consistent treatment of non-standard, dissipative effects that can alter the pattern of neutrino oscillations. In particular, initially massless neutrinos can give rise to a nonvanishing flavour transition probability, involving in addition the Majorana CP-violating mixing phase.Comment: 27 pages, plain-TeX, no figure