Related papers: Non-Commutative Complete Mellin Representation for…
Off-shell celestial amplitudes with both time-like and space-like external legs are defined. The Feynman rules for scalar amplitudes, viewed as a set of recursion relations for off-shell momentum space amplitudes, are transformed to the…
We present the exact solution of a scalar field theory defined with noncommuting position and momentum variables. The model describes charged particles in a uniform magnetic field and with an interaction defined by the Groenewold-Moyal…
Representations are derived for the basic scalar one-loop vertex Feynman integrals as meromorphic functions of the space-time dimension $d$ in terms of (generalized) hypergeometric functions $_2F_1$ and $F_1$. Values at asymptotic or…
The computational technique of $N$-fold Mellin-Barnes (MB) integrals, presented in a companion paper by the same authors, is used to derive sets of series representations of the massive one-loop conformal 3-point Feynman integral in various…
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner…
In this paper, we establish and employ a local framework to the first order of Riemann's curvature tensor in order to develop the corresponding coordinate non commutativity into general manifolds. We also exploit a new translation of…
It is well known that noncommutative geometry naturally emerges in the quantum Hall states due to the presence of strong and constant magnetic fields. Here, we discuss the underlying noncommutative geometry of quantum Hall fluids in which…
The finite and infinite harmonic sums form the general basis for the Mellin transforms of all individual functions $f_i(x)$ describing inclusive quantities such as coefficient and splitting functions which emerge in massless field theories.…
We present a method, based on Feynman path integrals, to describe the propagation and properties of the quantised electromagnetic field in an arbitrary, nonlinear medium. We provide a general theory, valid for any order of optical…
A new approach for arbitrary dimension to the Friedmann cosmological models is presented. Taking suitable changes of the parameters of the spacetime the harmonic motion equations appear, where the curvature determines the angular frequency.…
We present a new method for the decomposition of multi-loop Euclidean Feynman integrals into quasi-finite Feynman integrals. These are defined in shifted dimensions with higher powers of the propagators, make explicit both infrared and…
One particular approach to quantum groups (matrix pseudo groups) provides the Manin quantum plane. Assuming an appropriate set of non-commuting variables spanning linearly a representation space one is able to show that the endomorphisms on…
In this work, we investigate a very important but unstressed result in the work of Carl M. Bender, Jun-Hua Chen, and Kimball A. Milton ( J.Phys.A39:1657-1668, 2006). In this article, Bender \textit{et.al} have calculated the vacuum energy…
Different viewpoints on the asymptotic expansion of Feynman diagrams are reviewed. The relations between the field theoretic and diagrammatic approaches are sketched. The focus is on problems with large masses or large external momenta.…
The proper time path integral representation is derived explicitly for an arbitrary $n$-point amplitude in QCD. In the standard perturbation theory the formalism allows to sum up the leading subseries, e.g. yielding double-logarithm Sudakov…
We analyse in detail the quantization of a simple noncommutative model of spontaneous symmetry breaking in zero dimensions taking into account the noncommutative setting seriously. The connection to the counting argument of Feyman diagrams…
We study the commutative limit of the non-commutative maximally supersymmetric Yang-Mills theory in four dimensions (N=4 SYM). The commutative limits of non-commutative spaces are important in particular in the applications of…
Noncommutative field theories are a class of theories beyond the standard model of elementary particle physics. Their importance may be summarized in two facts. Firstly as field theories on noncommutative spacetimes they come with natural…
Quantum mechanics in a noncommutative plane is considered. For a general two dimensional central field, we find that the theory can be perturbatively solved for large values of the noncommutative parameter ($\theta$) and explicit…
We generalize the previously given algebraic version of "Feynman's proof of Maxwell's equations" to noncommutative configuration spaces. By doing so, we also obtain an axiomatic formulation of nonrelativistic quantum mechanics over such…