Related papers: A modern guide to {\rm $\theta$}-Poincar\'e
We investigate a quantum geometric space in the context of what could be considered an emerging effective theory from Quantum Gravity. Specifically we consider a two-parameter class of twisted Poincar\'e algebras, from which Lie-algebraic…
We consider a noncommutative field theory with space-time $\star$-commutators based on an angular noncommutativity, namely a solvable Lie algebra: the Euclidean in two dimension. The $\star$-product can be derived from a twist operator and…
We propose a stochastic interpretation of spacetime non-commutativity starting from the path integral formulation of quantum mechanical commutation relations. We discuss how the (non-)commutativity of spacetime is inherently related to the…
We give an introductory review of quantum physics on the noncommutative spacetime called the Groenewold-Moyal plane. Basic ideas like star products, twisted statistics, second quantized fields and discrete symmetries are discussed. We also…
The concept of a noncommutative field is formulated based on the interplay between twisted Poincar\'e symmetry and residual symmetry of the Lorentz group. Various general dynamical results supporting this construction, such as the…
A general formalism is developed that allows the construction of a field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime (Poincar\' e group) is replaced by a quantum group. This…
We report on a comprehensive analysis of the renormalization of noncommutative \phi^4 scalar field theories on the Groenewold-Moyal (GM) plane. These scalar field theories are twisted Poincar\'e invariant. Our main results are that these…
Lorentz covariance is the fundamental principle of every relativistic field theory which insures consistent physical descriptions. Even if the space-time is noncommutative, field theories on it should keep Lorentz covariance. In this…
In a recent paper, we have studied associative realizations of the noncommutative extended Snyder model, obtained by including the Lorentz generators (tensorial coordinates) and their conjugated momenta. In this paper, we extend this result…
Quantum theories constructed on the noncommutative spacetime called the Groenewold-Moyal(GM) plane exhibit many interesting properties such as causality violation, Lorentz and CPT non-invariance and twisted statistics. Such violations lead…
Quantisation of Lorentz invariant scalar field theory in Doplicher-Fredenhagen-Roberts (DFR) space-time, a Lorentz invariant, non-commutative space-time is studied. Absence of a unique Lagrangian in non-commutative space-time necessitates…
Here, we present an algebraic and kinematical analysis of non-commutative $\kappa$-Minkowski spaces within Galilean (non-relativistic) and Carrollian (ultra-relativistic) regimes. Utilizing the theory of Wigner-In\"{o}nu contractions, we…
Implementing Poincar\'e's `geometric conventionalism' a scalar Lorentz-covariant gravity model is obtained based on gravitationally modified Lorentz transformations (or GMLT). The modification essentially consists of an appropriate…
The concept of twisted Poincar\'e symmetry, as well as some implications, are reviewed. The spin-statistics relation and the nonlocality of NC QFT are discussed in the light of this quantum symmetry. The possibility of a twisted symmetry…
We study the possibility of introducing the classical analogue of Snyder's Lorentz-covariant noncommutative space-time in two-time physics theory. In the free theory we find that this is possible because there is a broken local scale…
Unified graded differential algebra, generated by $\kappa$-Minkowski noncommutative (NC) coordinates, Lorentz generators and anticommuting one-forms, is constructed. It is compatible with $\kappa$-Poincar\'e-Hopf algebra. For time- and…
It is argued that the familiar algebra of the non-commutative space-time with $c$-number $\theta^{\mu\nu}$ is inconsistent from a theoretical point of view. Consistent algebras are obtained by promoting $\theta^{\mu\nu}$ to an…
We consider Yang-Mills theories formulated on a non-commutative space-time described by a space-time dependent anti-symmetric field $\theta^{\mu\nu}(x)$. Using Seiberg-Witten map techniques we derive the leading order operators for the…
Noncommutativity of the spacetime coordinates has been explored in several contexts, mostly associated to phenomena at the Planck length scale. However, approaching this question through deformation theory and the principle of stability of…
In this paper we revisit the model of $\kappa$-deformed complex scalar field. We find that this model possesses ten conserved Noether charges that form, under commutators, a representation of (undeformed) Poincar\'e algebra. It follows that…