On Markovian cocycle perturbations in classical and quantum probability.
On path integration on noncommutative geometries
We discuss a recent approach to quantum field theoretical path integration on noncommutative geometries which imply UV/IR regularising finite minimal uncertainties in positions and/or momenta. One class of such noncommutative geometries arise as `momentum spaces' over curved spaces, for which we can now give the full set of commutation relations in coordinate free form, based on the Synge world function.
On quantum vector fields in general relativistic quantum mechanics.
On quantum weyl algebras and generalized quons
The model of generalized quons is described in an algebraic way as certain quasiparticle states with statistics determined by a commutation factor on an abelian group. Quantization is described in terms of quantum Weyl algebras. The corresponding commutation relations and scalar product are also given.
On the classical and quantum evolution of lagrangian half-forms in phase space
On the commutativity of two projections.
On the Correspondence Principle for the Quantized Annulus.
On the derivation and mathematical analysis of some quantum–mechanical models accounting for Fokker–Planck type dissipation: Phase space, Schrödinger and hydrodynamic descriptions
This paper is intended to provide the reader with a review of the authors’ latest results dealing with the modeling of quantum dissipation/diffusion effects at the level of Schrödinger systems, in connection with the corresponding phase space and fluid formulations of such kind of phenomena, especially in what concerns the role of the Fokker–Planck mechanism in the description of open quantum systems and the macroscopic dynamics associated with some viscous hydrodynamic models of Euler and Navier–Stokes...
On the evaluation of one-loop Feynman amplitudes in euclidean quantum field theory
On the Fock representation of the q-commutation relations.
On the Heisenberg-Weyl inequality.
On the product of self-adjoint operators.
On the second quantisation of Hilbert-Schmidt processes
On two quantum versions of the detailed balance condition
Quantum detailed balance conditions are often formulated as relationships between the generator of a quantum Markov semigroup and the generator of a dual semigroup with respect to a certain scalar product defined by an invariant state. In this paper we survey some results describing the structure of norm continuous quantum Markov semigroups on ℬ(h) satisfying a quantum detailed balance condition when the duality is defined by means of pre-scalar products on ℬ(h) of the form (s ∈ [0,1]) in order...
On two reverse inequalities in the Segal-Bargmann space.
Opérateurs d'échange et quelques applications des méthodes de noyaux
Operators of the q-oscillator
We scrutinize the possibility of extending the result of [19] to the case of q-deformed oscillator for q real; for this we exploit the whole range of the deformation parameter as much as possible. We split the case into two depending on whether a solution of the commutation relation is bounded or not. Our leitmotif is subnormality. The deformation parameter q is reshaped and this is what makes our approach effective. The newly arrived parameter, the operator C, has two remarkable properties: it...
Optimal Holomorphic Hypercontractivity for CAR Algebras
We present a new proof of Janson’s strong hypercontractivity inequality for the Ornstein-Uhlenbeck semigroup in holomorphic algebras associated with CAR (canonical anticommutation relations) algebras. In the one generator case we calculate optimal bounds for t such that is a contraction as a map for arbitrary p ≥ 2. We also prove a logarithmic Sobolev inequality.
Particles in the superworldline and BRST
In this short note we discuss -supersymmetric worldlines of relativistic massless particles and review the known result that physical spin- fields are in the first BRST cohomology group. For , emphasis is given to particular deformations of the BRST differential, that implement either a covariant derivative for a gauge theory or a metric connection in the target space seen by the particle. In the end, we comment about the possibility of incorporating Ramond-Ramond fluxes in the background.
Partition-dependent stochastic measures and -deformed cumulants.