arXiv subjects
Publications and source records attributed to R. Floreanini.
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.
We present some general considerations on possible experimental tests of Bell's locality in the neutral kaon system, and comment on the recent literature on the topic.
The neutral kaon system can be effectively described by non-unitary, dissipative, completely positive dynamics that extend the usual treatment. In the framework of open quantum systems, we show how the origin of these non-standard time evolutions can be traced to the interaction of the kaon system with a large environment. We find that D-branes, effectively described by a heat-bath of quanta obeying infinite statistics, could constitute a realistic example of such an environment.
It has been recently proposed to study generic dynamical evolutions of the neutral kaon system that go beyond quantum mechanics. We explicitly show that, unless the condition of complete positivity is enforced, those dynamics are physically inconsistent and should be rejected.
We use (nonconservative) dynamical semigroups to investigate the decay law of a quantum unstable system weakly coupled with a large environment. We find that the deviations from the classical exponential law are small and can be safely ignored in any actual experiment.
We formulate a set of Bell's inequalities for the system of two correlated neutral kaons coming from the decay of a phi-meson, without assuming CP and CPT invariance. We show that a non-vanishing value of the phenomenological parameter epsilon' would violate such inequalities, ruling out Bell's locality.
We study the behaviour of correlated neutral kaons produced in phi-meson decays under the hypothesis that the quantum mechanical time-evolution is completely positive. We show that planned experiments at phi-factories could give precise bounds on the phenomenological parameters of the model.
We study the modified dynamical evolution of the neutral kaon system under the condition of complete positivity. The accuracy of the data from planned future experiments is expected to be sufficiently precise to test such a hypothesis.
Available data on measured observables allow deriving estimates for some of the phenomenological parameters that characterize the time-evolution and decay of the neutral kaon system based on the hypothesis of complete positivity. The present experimental uncertainties are still too large to permit a full test of complete positivity.
Models that provide experimentally testable violations of ordinary Quantum Mechanics have been recently proposed. These models are based on non-unitary time evolutions of density matrices that are generated by linear positive maps. We discuss the consequences of imposing a stronger condition on those maps, known as complete positivity. It turns out that experimental data on the neutral kaon system giving upper bounds to the parameters characterizing positive maps, also give bounds to those determining completely positive ones.
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.
We discuss the definition of the average effective action in terms of the heat-kernel. As an example we examine a model describing a self-interacting scalar field, both in flat and curved background, and study the renormalization group flow of some of the parameters characterizing its effective potential. Some implications of the running of these parameters for inflationary cosmology are also briefly discussed.
We consider a scalar-metric gauge theory of gravity with independent metric, connection and dilaton. The role of the dilaton is to provide the scale of all masses, via its vacuum expectation value. In this theory, we study the renormalization group flow of the dilaton potential, taking into account threshold effects at the Planck scale. Due to the running of the VEV of the dilaton all particles that would naively seem to have masses larger than Planck's mass, may actually not propagate. This could solve the problem of unitarity in these theories.
In a four dimensional theory of gravity with lagrangian quadratic in curvature and torsion, we compute the effective action for metrics of the form $g_{μν}=ρ^2δ_{μν}$, with $ρ$ constant. Using standard field-theoretic methods we find that one loop quantum effects produce a nontrivial effective potential for $ρ$. We explain this unexpected result by showing how our regularization procedure differs from the one that is usually adopted in Quantum Gravity. Using the method of the average effective potential, we compute the scale dependence of the v.e.v. of the conformal factor.
The positive-energy unitary irreducible representations of the $q$-deformed conformal algebra ${\cal C}_q = {\cal U}_q(su(2,2))$ are obtained by appropriate deformation of the classical ones. When the deformation parameter $q$ is $N$-th root of unity, all these unitary representations become finite-dimensional. For this case we discuss in some detail the massless representations, which are also irreducible representations of the $q$-deformed Poincaré subalgebra of ${\cal C}_q$. Generically, their dimensions are smaller than the corresponding finite-dimensional non-unitary representation of $su(2,2)$, except when $N=2$, $h=0$ and $N = 2 \vert h\vert +1$, where $h$ is the helicity of the representations. The latter cases include the fundamental representations with $h = \pm 1/2$.
The algebra W_{1+\infty} with central charge c=0 can be identified with the algebra of quantum observables of a particle moving on a circle. Mathematically, it is the universal enveloping algebra of the Euclidean algebra in two dimensions. Similarly, the super W_\infty algebra is found to be the universal enveloping algebra of the super-Euclidean algebra in two dimensions.
The connection between q-analogs of special functions and representations of quantum algebras has been developed recently. It has led to advances in the theory of q-special functions that we here review.