Related papers: Quantum causality in $\kappa$-Minkowski and relate…
In causal set theory, there are three ambiguous concepts that this article tries to provide a solution to resolve these ambiguities. These three ambiguities in Planck's scale are: the causal relationship between events, the position of the…
We study the spectral dimension associated with diffusion processes on Euclidean $\kappa$-Minkowski space. We start by describing a geometric construction of the "Euclidean" momentum group manifold related to $\kappa$-Minkowski space. On…
We argue that superluminal signal propagation is possible in consistent Poincare invariant quantum field theories in two space-time dimensions, provided spatial parity is broken. This happens due to existence of the ``instantaneous'' causal…
The theory of the $\kappa$-deformed Poincare algebra is applied to the analysis of various phenomena in special relativity, quantum mechanics and field theory. The method relies on the development of series expansions in $\kappa^{-1}$ of…
We introduce a novel class of quantum circuits that are unitary along three distinct "arrows of time". These dynamics share some of the analytical tractability of "dual-unitary" circuits, while exhibiting distinctive and richer…
We show that there exists a canonical topology, naturally connected with the causal site of J. D. Christensen and L. Crane, a pointless algebraic structure motivated by quantum gravity. Taking a causal site compatible with Minkowski space,…
The notion of a K\"ahler structure for a differential calculus was recently introduced by the second author as a framework in which to study the noncommutative geometry of the quantum flag manifolds. It was subsequently shown that any…
Motivated by the classical Euler elastic curves, David A. Singer posed in 1999 the problem of determining a plane curve whose curvature is given in terms of its position. We propound the same question in Lorentz-Minkowski plane, focusing on…
We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…
A modified version of the bilocal particle is presented in terms of complex space time. Unusual constraint structure of the model is studied, and a new concept of the physical equivalence is proposed in accordance with Dirac's conjecture.…
In this study, we construct a 1+1-dimensional, relativistic, free, complex scalar Quantum Field Theory on the noncommutative spacetime known as lightlike $\kappa$-Minkowski. The associated $\kappa$-Poincar\'e quantum group of isometries is…
Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d-dimensional conformal field theory, we show how such constraints are encoded in…
I discuss the idea of relativistic causality, i.e. the requirement that causal processes or signals can propagate only within the light-cone. After briefly locating this requirement in the philosophy of causation, my main aim is to draw…
This article demonstrates how the transition from a (Riemannian) twisted spectral triple to a pseudo-Riemannian spectral triple arises within an almost-commutative spectral triple. This opens a new perspective on the Lorentzian signature…
Defining a new r-matrix compatible with the scalar product at the basis of the Chern-Simons action for a particle coupled to (2+1) Lorentzian gravity with cosmological constant, I show how deformed symmetries of $\kappa$-de Sitter and, in…
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…
We use factorisations of the local isometry groups arising in 3d gravity for Lorentzian and Euclidean signatures and any value of the cosmological constant to construct associated bicrossproduct quantum groups via semidualisation. In this…
We analyze the response of a detector with a uniform acceleration $\alpha$ in $\kappa-$Minkowski spacetime using the first order perturbation theory. The monopole detector is coupled to a massless complex scalar field in such a way that it…
A quantum deformation of the conformal algebra of the Minkowskian spacetime in $(3+1)$ dimensions is identified with a deformation of the $(4+1)$-dimensional AdS algebra. Both Minkowskian and AdS first-order non-commutative spaces are…
We shall outline two ways of introducing the modification of Einstein's relativistic symmetries of special relativity theory - the Poincar\'{e} symmetries. The most complete way of introducing the modifications is via the noncocommutative…