Related papers: Generalized commutation relations and Non linear m…

In this paper, I develop the Soldering formalism in a new domain - the noncommutative planar field theories. The Soldering mechanism fuses two distinct theories showing opposite or complimentary properties of some symmetry, taking into…

We present a short introductory overview of the non-commutative extensions of several classical physical theories. After a general discussion of the reasons that suggest that the non-commutativity is a major issue that will eventually lead…

Recent developments on emergence of logarithmic terms in correlators or response functions of models which exhibit dynamical symmetries analogous to conformal invariance in not necessarily relativistic systems are reviewed. The main…

In this paper we discuss how the Magueijo-Smolin Doubly Special Relativity proposal may obtained from a singular Lagrangian action. The deformed energy-momentum dispersion relation rises as a particular gauge, whose covariance imposes the…

This work reports on the construction of a nonlinear distributional geometry (in the sense of Colombeau's special setting) and its applications to general relativity with a special focus on the distributional description of impulsive…

Recently there have been several studies devoted to the investigation of the fate of fundamental relativistic symmetries at the foreseen unification of gravity and quantum regime, that is the Planck scale. In order to preserve covariance of…

The non-commutative five-term relation $T_{1,0} T_{0,1} = T_{0,1} T_{1,1} T_{1,0}$ is shown to hold for certain operators acting on symmetric functions. The "generalized recursion" conjecture of Bergeron and Haiman is a corollary of this…

We study the dynamical features of Maggiore's generalised commutation relations. We focus on their generality and, in particular, their dependence on the Hamiltonian H. We derive the generalisation of the Planck's law for black body…

Using the notion of a gauge connection on a flat superspace, we construct a general class of noncommutative ($D=2,$ $\mathcal{N}=1$) supertranslation algebras generalizing the ordinary algebra by inclusion of some new bosonic and fermionic…

In this paper we review the extent to which one can use classical distribution theory in describing solutions of Einstein's equations. We show that there are a number of physically interesting cases which cannot be treated using…

First, we point out that the present applied superposition principle is linear, it must be developed into a generality. Next, the linear operators and equations should be developed nonlinearly. They will include nonlinear Klein-Gordon…

We revisit the generalized connection of Double Field Theory. We implement a procedure that allow us to re-write the Double Field Theory equations of motion in terms of geometric quantities (like generalized torsion and non-metricity…

Using perturbation theory, we explore the universal high momentum behavior of correlation functions of gauge invariant operators in planar noncommutative gauge theories. We find that the correlation functions are strongly enhanced when…

For a semi-linear Schr\"{o}dinger equation of Hartree type in three spatial dimensions, various approximations of singular, point-like perturbations are considered, in the form of potentials of very small range and very large magnitude,…

A new type of a nonlinear gauge quantum theory (superrelativity) has been proposed. Such theory demands a radical reconstruction of both the quantum field conception and spacetime structure, and this paves presumably way to the…

An intriguing connection, based on duality symmetry, between ordinary (commutative) Born-Infeld type theory and non-commutative Maxwell type theory, is pointed out. Both discrete as well as continuous duality transformations are considered…

We review the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and…

Representations by linear integral operators on $L_p$ spaces over measure spaces are investigated for the polynomial covariance type commutation relations and more general two-sided generalizations of covariance commutation relations…

Generalized Functions play a central role in the understanding of differential equations containing singularities and nonlinearities. Introducing infinitesimals and infinities to deal with these obstructions leads to controversies…

We propose a deformed version of the generalized Heisenberg algebra by using techniques borrowed from the theory of pseudo-bosons. In particular, this analysis is relevant when non self-adjoint Hamiltonians are needed to describe a given…