Related papers: Geometry of physical dispersion relations

This paper presents the fascinating correspondence between the geometric function theory and the scattering amplitudes with $O(N)$ global symmetry. A crucial ingredient to show such correspondence is a fully crossing symmetric dispersion…

Systems consisting of identical bosons with a large scattering length satisfy universal relations determined by 2-body physics that are similar to those for fermions with two spin states. They require the momentum distribution to have a…

It is shown that calculus can apply on a fractal structure with the condition that the infinitesimal limit of change of the variable is larger than the lower cut-off of the fractal structure, and an assumption called local decomposability.…

The geometrical picture of gauge theories must be enlarged when a gauge potential ceases to behave like a connection, as it does in electroweak interactions. When the gauge group has dimension four, the vector space isomorphism between…

In the framework of multiple-scattering theory, we show that the dispersion relations of certain electromagnetic (EM) and elastic metamaterials can be obtained analytically in the long-wavelength limit. Specific examples are given to the…

In this paper, after a brief review of the general theory of dispersive waves in dissipative media, we present a complete discussion of the dispersion relations for both the ordinary and the time-fractional Cattaneo-Maxwell heat equations.…

In the context of departures from Special Relativity written as a momentum power expansion in the inverse of an ultraviolet energy scale M, we derive the constraints that the relativity principle imposes between coefficients of a deformed…

The Ehresmann connection on a fiber bundle that is not compatible with a (possible) Lie group structure is illustrated by the geometry of a general anholonomic observer in the Minkowski space. The 3D split of Maxwell's equations induces…

We propose a new model for the description of a gravitating multi particle system, viewed as a kinetic gas. The properties of the, colliding or non-colliding, particles are encoded into a so called one-particle distribution function, which…

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…

We have discovered that two significant quantities within hard particle systems: the probability of successfully inserting an additional particle at random and the scale distribution function, can be connected by a concise relation. We…

We investigate when the tangent bundle of a projective manifold has a non-trivial first order (or positive-dimensional) deformation. This leads to a new conjectural characterization of the complex projective space.

In a fibre bundle, natural derivatives of a section are defined as tangent vector fields on the image of a section of the fibre bundle. A local extension to vector fields in the tangent bundle leads to a direct proof of the formula…

Remnant low-energy effects of Planck-scale Lorentz breaking in candidate fundamental theories typically include modified one-particle dispersion relations. Theoretical constraints on such modifications are discussed leading to the exclusion…

The mathematical properties associated with the widely accepted concept of the extensivity of many of the common thermodynamic variables are examined and some of their consequences considered. The possible conflict between some of these and…

In this work, the poles and the resulting dispersion spectra from the relativistic kinetic equation have been analyzed with the help of a proposed collision kernel that conserves both the energy-momentum tensor and particle current by…

We establish that two-dimensional dipolar quantum gases admit a universal description, i.e., their thermodynamic properties are independent of details of the interaction at short distances. The only relevant parameters are the dipole length…

Making use of a recursive approach, derivative dispersion relations are generalized for an arbitrary number of subtractions. The results for both cross even and odd amplitudes are theoretically consistent at sufficiently high energies and…

Using the logarithmic superfluid model of physical vacuum, one can formulate a quantum theory, which successfully recovers Einstein's theory of relativity in low-momenta limit, but otherwise has different foundations and predictions. We…

The automorphism invariant theory of Crawford[J. Math. Phys. 35, 2701 (1994)] has show great promise, however its application is limited by the paradigm to the domain of spin space. Our conjecture is that there is a broader principle at…