Related papers: Geometry of physical dispersion relations
The covariant understanding of dispersion relations as level sets of Hamilton functions on phase space enables us to derive the most general dispersion relation compatible with homogeneous and isotropic spacetimes. We use this concept to…
The conditions for observation of the particle coordinates, required by logic of the Special Relativity and filtering the quantum field effects, are described. A general relation between the corresponding density of probability and the wave…
We introduce a conditional pair distribution function (CPDF) which characterizes the probability density of finding an object (e.g., a particle in a fluid) to certain distance of other, with each of these two having a nearest neighbor to a…
We analyze a few illustrative examples of scenarios in which relativistic symmetries are deformed by Planck-scale effects in particle-type-dependent manner. The novel mathematical structures required by such scenarios are the mixing…
When describing elastic deformations of a body sometimes it is worth to take in account elastic spatial dispersion. If spatial dispersion is weak, as usually happens, then it can be reduced to dependence of thermodynamic potential on strain…
The deformation of the relativistic dispersion relation caused by noncommutative (NC) Quantum Mechanics (QM) is studied using the extended phase-space formalism. The introduction of the additional commutation relations induces Lorentz…
Various properties of fluids consisting of platelike particles differ from the corresponding ones of fluids consisting of spherical particles because interactions between platelets depend on their mutual orientations. One of the main issues…
It is shown that quantum entanglement is the only force able to maintain the fourth state of matter, possessing fixed shape at an arbitrary volume. Accordingly, a new relativistic Schrodinger equation is derived and transformed further to…
A generalized formulation of non-relativistic quantum mechanics is developed within multidimensional geometric (NG) frameworks characterized by a power-law dispersion relation \(E \propto |p|^{j}\), where \(j = N - 1\). Starting from the…
Recent attempts to determine the pion polarizability by dispersion relations yield values that disagree with the predictions of chiral perturbation theory. These dispersion relations are based on specific forms for the absorptive part of…
Based on the Tsallis entropy, the nonextensive thermodynamic properties are studied as a q-deformation of classical statistical results using only probabilistic methods and straightforward calculations. It is shown that the constant in the…
The traces of gauge-covariant Sobolev spaces on a Riemannian vector bundle for some connection are characterised as some gauge-covariant fractional Sobolev spaces when the curvature of the connection is bounded. The constants in the trace…
In a recent paper (arXiv:1412.6000) a general mechanism for emergence of cosmological space-time geometry from a quantum gravity setting was devised and departure from standard dispersion relations for elementary particle were predicted. We…
The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interaction force kernels by utilizing a compactness convergence…
The polygonal distributions are a class of distributions that can be defined via the mixture of triangular distributions over the unit interval. The class includes the uniform and trapezoidal distributions, and is an alternative to the beta…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
The underlying mathematical structures of gauge theories are known to be geometrical in nature and the local and global features of this geometry have been studied for a long time in mathematics under the name of fibre bundles. It is now…
Dispersion relations for the scattering of hadrons are considered within the framework of Quantum Chromodynamics. It is argued that the original methods of proof remain applicable. The setting and the spectral conditions are provided by an…
We take advantage of the principal bundle geometry of the space of connections to obtain general results on the presymplectic structure of two classes of (pure) gauge theories: invariant theories, and non-invariant theories satisfying two…
Galaxies and clusters distributions show two major properties: (i) the positions of galaxies and clusters are characterized by a power law distribution indicating properties with respect to their positions. (ii) The distribution of masses…