A recurrence relation approach to higher order quantum superintegrability.
Axiomatic quantum field theory in terms of operator product expansions: general framework, and perturbation theory via Hochschild cohomology.
-cross products and a generalized quantum mechanical -body problem.
Decoherence of quantum Markov semigroups
Derivations of quasi -algebras.
Differential representations of dynamical oscillator symmetries in discrete Hilbert space.
Extension of the Poincaré symmetry and its field theoretical implementation.
Extension techniques in -cross products by compact group duals and in quantum field theory.
Field-theoretic Weyl deformation quantization of enlarged Poisson algebras.
Formula for unbiased bases
The present paper deals with mutually unbiased bases for systems of qudits in dimensions. Such bases are of considerable interest in quantum information. A formula for deriving a complete set of mutually unbiased bases is given for where is a prime integer. The formula follows from a nonstandard approach to the representation theory of the group . A particular case of the formula is derived from the introduction of a phase operator associated with a generalized oscillator algebra. The case...
Generalized deformed commutation relations with nonzero minimal uncertainties in position and/or momentum and applications to quantum mechanics.
Generalized Heisenberg algebras, SUSYQM and degeneracies: infinite well and Morse potential.
Hidden symmetry from supersymmetry in one-dimensional quantum mechanics.
Junction type representations of the Temperley-Lieb algebra and associated symmetries.
Non-commutative Markov processes in free groups factors, related to Berezin's quantization and automorphic forms.
On spin and modularity in conformal field theory
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.
Para-Grassmann variables and coherent states.
Pseudo-bosons from Landau levels.
Quadratic algebra approach to an exactly solvable position-dependent mass Schrödinger equation in two dimensions.