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...

The non-commutative geometric construction of A. Connes [1-5] has been successful in giving a geometrical interpretation of the standard model as well as some grand unification models. Our lack of ability to quantize the non-commutative actions forced on us to quantize the classical actions resulting from the non-commutative ones by adopting the usual rules. The symmetries that might be present...

In this paper we have studied a new Non-Commutative (NC) space with an operatorial form of noncommutativity. A point particle in this space feels the interaction of a magnetic field, that is singular at a specific position θ −1. Here θ is the NC parameter and plays the role of particle charge as well. The magnetic moment of the particle is computed and its dynamics is studied in detail, both fr...

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...

In this survey we present the appearance of some combinatorial notions in quantum field theory. We first focus on graph polynomials (the Tutte polynomial and its multivariate version) and their relation with the parametric representation of the commutative Φ field theory. We then generalize this to ribbon graphs and present the relation of the Bollobás–Riordan polynomial with the parametric rep...

A normed space $mathfrak{X}$ is said to have the fixed point property, if for each nonexpansive mapping $T : E longrightarrow E $ on a nonempty bounded closed convex subset $ E $ of $ mathfrak{X} $ has a fixed point. In this paper, we first show that if $ X $ is a locally compact Hausdorff space then the following are equivalent: (i) $X$ is infinite set, (ii) $C_0(X)$ is infinite dimensional, (...