Noncommutative Chern-Simons theory can be classically mapped to commutative Chern-Simons theory by the Seiberg-Witten map. We provide evidence that the equivalence persists at the quantum level by computing two and three-point functions of field strengths on the commutative side and their Seiberg-Witten transforms on the noncommutative side to the first nontrivial order in perturbation theory. ...

The groupoid approach to noncommutative unification of general relativity with quantum mechanics is compared with the canonical gravity quantization. It is shown that by restricting the corresponding noncommutative algebra to its (commutative) subalgebra, which determines the space-time slicing, an algebraic counterpart of superspace (space of 3-metrics) can be obtained. It turns out that when ...

We review some selected aspects of the construction of gauge invariant operators in field theories on non-commutative spaces and their relation to the energy momentum tensor as well as to the non-commutative loop equations. To appear in the Proceedings of the RTN meeting “The Quantum Structure of Spacetime and the Geometric Nature of Fundamental Interactions”, Corfu, September 13-20, 2001 dorn@...

Nicolas Privault Abstract The aim of this note is to introduce a calculus on Fock space with its probabilistic interpretations, and to give a detailed presentation of the associated quantum Itô formula. Calcul sur l’espace de Fock et une formule d’Itô non-commutative anticipante Résumé Le but de cette note est d’introduire un calcul sur l’espace de Fock et de donner une présentation détaillée d...

2014 In contradiction to the prediction of the Periodic Table but in agreement with earlier suggestions by Brewer and Mann, the ground state configuration of atomic Lawrencium (Z = 103) will not be 7s2 6d 2D3/2 but 7s2 7p 2P1/2. The reason for this deviation from normal trends across the Periodic Table are strong relativistic effects on the outermost 7p1/2 orbital. Multiconfiguration Dirac-Fock...

We investigate the impact of rotational diffusion on the electrodynamic coupling of fluorescent dye molecules (oscillating electric dipoles) to a tunable planar metallic nanocavity. Fast rotational diffusion of the molecules leads to a rapidly fluctuating mode density of the electromagnetic field along the molecules' dipole axis, which significantly changes their coupling to the field as compar...

Quantum mechanics is, viewed purely as a mathematical theory, a generalisation of probability theory (a non-commutative probability theory). Application to a concrete problem however, reduces the theory to a probability theory in the classical sense [1, p. 280]. Quantum Mechanics thus (only) aspires to yield expectation values and probability distributions for the outcomes of statistical experi...

Starting from the concept of the universal exterior algebra in non-commutative differential geometry we construct differential forms on the quantum phase-space of an arbitrary system. They bear the same natural relationship to quantum dynamics which ordinary tensor fields have with respect to classical hamiltonian dynamics.

We extend the parametric representation of renormalizable non commutative quantum field theories to a class of theories which we call “critical”, because their power counting is definitely more difficult to obtain.This class of theories is important since it includes gauge theories, which should be relevant for the quantum Hall effect.

Quantum-like evolution laws for observables can be derived from classical Hamiltonian equations with the only additional assumption that the phase space is non-commutative. The derivation is possible for Hamiltonians that are polynomial functions in position and momentum variables, and supports the use of phase space distributions functions in both quantum and classical theories that rely on ex...