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We present a method to accelerate the numerical evaluation of spatial integrals of Feynman diagrams when expressed on the real frequency axis. This can be realized through use of a renormalized perturbation expansion with a constant but…
We describe the scalar and spinor fields on noncommutative sphere starting from canonical realizations of the enveloping algebra ${\cal A}={\cal U}{u(2))}$. The gauge extension of a free spinor model, the Schwinger model on a noncommutative…
A very first step to develop non-commutative algebraic geometry is the arithmetic of polynomials in non-commuting variables over a commutative field, that is, the study of elements in free associative algebras. This investigation is…
We show that 2D noncommutative harmonic oscillator has an isotropic representation in terms of commutative coordinates. The noncommutativity in the new mode, induces energy level splitting, and is equivalent to an external magnetic field…
Perturbative expansions in many physical systems yield 'only' asymptotic series which are not even Borel resummable. Interestingly, the corresponding ambiguities point to nonperturbative physics. We numerically verify this renormalon…
BFYM on commutative and noncommutative ${\mathbb{R}}^4$ is considered and a Seiberg-Witten gauge-equivalent transformation is constructed for these theories. Then we write the noncommutative action in terms of the ordinary fields and show…
A free spinor field on a noncommutative sphere is described starting from a canonical realization of the enveloping algebra U(u(2|1)). The gauge extension of the model - the Schwinger model on a noncommutative sphere is defined and the…
The non-commutative O(N) Gross-Neveu model is solved in the large N limit in two and three space-time dimensions. The commutative version of the two dimensional model is a renormalizable quantum field theory, both in a coupling constant…
The Koopman framework is a popular approach to transform a finite dimensional nonlinear system into an infinite dimensional, but linear model through a lifting process, using so-called observable functions. While there is an extensive…
This paper addresses three topics concerning the quantization of non-commutative field theories (as defined in terms of the Moyal star product involving a constant tensor describing the non-commutativity of coordinates in Euclidean space).…
This paper summarizes the contents of the paper "Non-Commutative Worlds" by the author (published in New Journal of Physics Vol. 6, November 2004, pp. 2 - 46; quant-ph/0403012) and gives a new derivation of our generalization of…
The representations of the algebra of coordinates and momenta of noncommutative phase space are given. We study, as an example, the harmonic oscillator in noncommutative space of any dimension. Finally the map of Sch$\ddot{o}$dinger…
We apply the non-commutative Fourier transform for Lie groups to formulate the non-commutative metric representation of the Ponzano-Regge spin foam model for 3d quantum gravity. The non-commutative representation allows to express the…
We explore the Mellin representation of correlation functions in conformal field theories in the weak coupling regime. We provide a complete proof for a set of Feynman rules to write the Mellin amplitude for a general tree level Feynman…
We introduce a new model of spin noncommutative space in which noncommutative extension of the coordinate operators are assumed to be chirality dependent. Noncommutative correspondences of classical fields are defined via Weyl ordering, and…
An $\alpha$-parameter representation is derived for gauge field theories.It involves, relative to a scalar field theory, only constants and derivatives with respect to the $\alpha$-parameters. Simple rules are given to obtain the…
A review is given of some 2-dimensional metrics for which noncommutative versions have been found. They serve partially to illustrate a noncommutative extension of the moving-frame formalism. All of these models suggest that there is an…
The non-planar Feynman diagram with seven massless, scalar propagators and four on-shell legs (the crossed double box) is calculated analytically in dimensional regularization. The non-planar diagram with six propagators is also discussed.
These are lecture notes for an introductory course on noncommutative field and gauge theory. We begin by reviewing quantum mechanics as the prototypical noncommutative theory, as well as the geometrical language of standard gauge theory.…
I describe a novel covariant formulation of massive gauge theories in which the longitudinal polarization vectors do not grow with the energy. Therefore in the present formalism, differently from the ordinary one, the energy and coupling…