Related papers: Noncommutative geometrical origin of the energy-mo…
We propose a geometric framework where dispersion relations are viewed as parametric surfaces in energy-momentum space. Within this picture, the presence and type of critical points of the surface emerge as clear geometric signatures of…
The specification of energy for gravitating systems has been an unsettled issue since Einstein proposed his pseudotensor. It is now understood that energy-momentum is \emph{quasi-local} (associated with a closed 2-surface). Here we consider…
We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on…
We study field theories on the noncommutative Minkowski space with noncommuting time. The focus lies on dispersion relations in quantized interacting models in the Yang-Feldman formalism. In particular, we compute the two-point correlation…
From the constructions of the quantum spacetime, a four dimensional quantized spacetime can be embedded in a five dimensional continuous spacetime. Thus to observe from the five dimensional continuous spacetime where the four dimensional…
We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this…
We study noncommutative deformations of the wave equation in curved backgrounds and discuss the modification of the dispersion relations due to noncommutativity combined with curvature of spacetime. Our noncommutative differential geometry…
We derive a generalized Minkowski Energy Momentum Tensor for a monochromatic wave in a lossless medium exhibiting temporal and spatial dispersion. The Energy Momentum Tensor is then related to familiar expressions for energy density and…
A useful concept in the development of physical models on the $\kappa$-Minkowski noncommutative spacetime is that of a curved momentum space. This structure is not unique: several inequivalent momentum space geometries have been identified.…
We describe the Hamilton geometry of the phase space of particles whose motion is characterised by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a…
Consider the quasi-commutative approximation to a noncommutative geometry. It is shown that there is a natural map from the resulting Poisson structure to the Riemann curvature of a metric. This map is applied to the study of high-frequency…
We study potentially observable consequences of spatiotemporal discreteness for the motion of massive and massless particles. First we describe some simple intrinsic models for the motion of a massive point particle in a fixed causal set…
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…
The usual pre-metric Maxwell equations of electromagnetism in Minkowski space are extended to five dimensions, and the equations of linear five-dimensional electromagnetic waves are obtained from them by using the simplest electromagnetic…
Time-space noncommutativity leads to quantisation of time and energy nonconservation when time is conjugate to a compact spatial direction like a circle. In this context energy is conserved only modulo some fixed unit. Such a possibility…
Moeller's energy-momentum complex is employed in order to determine the energy and momentum distributions for a spacetime described by a "generalized Schwarzschild" geometry in (3+1)-dimensions on a noncommutative curved D3-brane in an…
We analyze the leading terms of the spectral action for a model of noncommutative geometry, which is a product of $4$-dimensional Riemannian manifold with a two-point space exploring the previously neglected case when the metrics over each…
Smooth deformations of a Minkowski type metric in a four-dimensional space-time manifold are considered. Deformations of the basic spin-tensorial fields associated with this metric are calculated and their application to calculating the…
The form of the energy-momentum tensor when a quasimonochromatic field propagates into and through an antireflection-coated, sourceless, transparent, continuous, linear magneto-dielectric medium, initially at rest in the local frame,…
We show that the relativistic energy-momentum relation can emerge as an effective ensemble-averaged structure from a multiplicative Hamiltonian when fluctuations of an auxiliary parameter are treated using maximum entropy inference. The…