Related papers: CPT breaking in noncommutative Magueijo-Smolin mod…
We introduce noncommutative phase spaces by minimal couplings (usual one, dual one and their mixing). We then realize some of them as coadjoint orbits of the anisotropic Newton-Hooke groups in two- and three-dimensional spaces. Through…
We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a non-relativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical…
We extend the class of QM problems which permit for quasi-exact solutions. Specifically, we consider planar motion of two interacting charges in a constant uniform magnetic field. While Turbiner and Escobar-Ruiz (2013) addressed the case of…
A model of a two-sheeted universe in the quantum theory of gravity is proposed, based on the definition of 3D invariant and gauge-invariant proper time of the universe. A uniform time in a closed universe is introduced in the class of…
We describe a new type of gravity-matter models where gravity couples in a non-conventional way to two distinct scalar fields providing a unified Lagrangian action principle description of: (a) the evolution of both "early" and "late"…
We study $2\times 2$ matrices over noncommutative rings with anti-involution, with a special focus on the symplectic group $\mathrm{Sp}_2(\mathcal{A},\sigma)$. We define traces and determinants of such matrices and use them to prove a…
We examine noninvertible symmetry (NIS) in one-dimensional (1D) symmetry-protected topological (SPT) phases protected by dipolar and exponential-charge symmetries, which are two key examples of modulated SPT (MSPT). To set the stage, we…
In this paper we have constructed a coordinate space (or geometric) Lagrangian for a point particle that satisfies the exact Doubly Special Relativity (DSR) dispersion relation in the Magueijo-Smolin framework. Next we demonstrate how a…
Extending earlier work(*), we examine the deformation of the canonical symplectic structure in a cotangent bundle $T^\star(\Q)$ by additional terms implying the Poisson non-commutativity of both configuration and momentum variables. In this…
In this article, an alternative interpretation of the Seiberg-Witten map in non-commutative field theory is provided. We show that the Seiberg-Witten map can be induced in a geometric way, by a field dependent co-ordinate transformation…
From a geometrical point of view it is, so far, not sufficiently well understood what should be a "noncommutative principal bundle". Still, there is a well-developed abstract algebraic approach using the theory of Hopf algebras. An…
The dissertation presents possibilities of applying noncommutative spacetimes description, particularly kappa-deformed Minkowski spacetime and Drinfeld's deformation theory, as a mathematical formalism for Doubly Special Relativity theories…
We describe an algebraic approach to the time-dependent noncommutative geometry of a six-dimensional Cahen-Wallach pp-wave string background supported by a constant Neveu-Schwarz flux, and develop a general formalism to construct and…
Noncommutative geometry allows to unify the basic building blocks of particle physics, Yang-Mills-Higgs theory and General relativity, into a single geometrical framework. The resulting effective theory constrains the couplings of the…
Certain supersymmetric sigma models in 2+1 dimensions feature multi-soliton solutions, with and without scattering. We subject these systems to a non-anticommutative deformation by replacing the Grassmann algebra of the odd superspace…
It is possible that relativistic symmetries become deformed in the semiclassical regime of quantum gravity. Mathematically, such deformations lead to the noncommutativity of spacetime geometry and non-vanishing curvature of momentum space.…
In this work, we comment on two special points in the paper by S. Ghosh [Phys. Rev. D 74, 084019 (2006)]. First of all, the Lagrangian presented by the author does not describe the Magueijo- Smolin model of Doubly Special Relativity since…
This review is devoted to the Multiple Point Principle (MPP), according to which several vacuum states with the same energy density exist in Nature. The MPP is implemented to the Standard Model (SM), Family replicated gauge group model…
Following our earlier work \cite{sunandan1, sunandan2}, we derive noncommuting phase-space structures which are combinations of both the $\kappa$-Minkowski and Snyder algebra by exploiting the reparametrisation symmetry of the recently…
We review the noncommutative approach to the standard model. We start with the introduction if the mathematical concepts necessary for the definition of noncommutative spaces, and manifold in particular. This defines the framework of…