Related papers: Finsler-like structures from Lorentz-breaking clas…
We study some physical consequences of the introduction of a Lorentz-violating modification term in the linearized gravity, which leads to modified dispersion relations for gravitational waves in the vacuum. We discuss two possible…
The second-order differential equation describes harmonic oscillators, as well as currents in LCR circuits. This allows us to study oscillator systems by constructing electronic circuits. Likewise, one set of closed commutation relations…
The correspondence principle in physics between quantum mechanics and classical mechanics suggests deep relations between spectral and geometric entities of Riemannian manifolds. We survey---in a way intended to be accessible to a wide…
A number of different approaches to quantum gravity are at least partly phenomenologically characterized by their treatment of Lorentz symmetry, in particular whether the symmetry is exact or modified/broken at the smallest scales. For…
Section 1 refines the theory of harmonic and potential maps. Section 2 defines a generalized Lorentz world-force law and shows that any PDEs system of order one generates such a law in suitable geometrical structure. In other words, the…
These are introductory notes on symmetries in quantum field theory and how they apply to particle physics. The notes cover the fundamentals of group theory, their representations, Lie groups, and Lie algebras, along with an elaborate…
Some of the most outstanding questions in the field of gravitation and geometry remain unsolved as a result of our limited understanding of the global structure of the spacetime geometry and the role played by global spacetime…
One of the difficulties encountered when studying physical theories in discrete space-time is that of describing the underlying continuous symmetries (like Lorentz, or Galilei invariance). One of the ways of addressing this difficulty is to…
In the framework of the spatial coherence wavelets, different features of the first-order spatial coherence (Young's interference) are analysed by calculating the corresponding marginal power spectrum, a close related quantity to the…
The relentless efforts of the physics community has not yet availed us the solution of how to unify the Quantum Mechanics with General Relativity, a puzzle that has engaged the minds of the physicists for almost a century. The insufficiency…
I here investigate what is arguably the most significant residual challenge for the proposal of phenomenologically viable "DSR deformations" of relativistic kinematics, which concerns the description of composite particles, such as atoms.…
The irreducible representations of the extended Galilean group are used to derive infinite sets of symmetric and asymmetric second-order differential equations with constant coeffcients. All derived equations are local and their Lagrangians…
Classical light bending is investigated for weak gravitational fields in the presence of hypothetical local Lorentz violation. Using an effective field theory framework that describes general deviations from local Lorentz invariance, we…
In Lorentz-violating electrodynamics a steady current (and similarly a static charge) generates both static magnetic and electric fields. These induced fields, acting on interfering particles, change the interference pattern. We find that…
In a recent paper we demonstrated how the simplest model for varying alpha may be interpreted as the effect of a dielectric material, generalized to be consistent with Lorentz invariance. Unlike normal dielectrics, such a medium cannot…
We consider a classical test particle subject to electromagnetic and gravitational fields, described by a Lagrangian depending on the acceleration and on a fundamental length. We associate to the particle a moving local reference frame and…
We study some properties of a recently proposed local Lorentz Violating Finsler geometry, the so-called Bipartite space. This anisotropic structure deforms the causal null surface to an elliptic cone and provides an anisotropy to the…
The purpose of this paper is to explain the phenomenon of symmetry breaking for optimal functions in functional inequalities by the numerical computations of some well chosen solutions of the corresponding Euler-Lagrange equations. For many…
We discuss three manners to implement Lorentz symmetry breaking in a superfield theory formulated within the superfield formalism, that is, deformation of the supersymmetry algebra, introducing of an extra superfield whose components can…
While conformal transformations of the plane preserve Laplace's equation, Lorentz-conformal mappings preserve the wave equation. We discover how simple geometric objects, such as quadrilaterals and pairs of crossing curves, are transformed…