Doubly Special Relativity and Finsler geometry

We discuss the recent proposal of implementing Doubly Special Relativity in configuration space by means of Finsler geometry. Although this formalism leads to a consistent description of the dynamics of a particle, it does not seem to give a complete description of the physics. In particular, the Finsler line element is not invariant under the deformed Lorentz transformations of Doubly Special Relativity. We study in detail some simple applications of the formalism.Comment: 8 pages, plain Te

A Novel Combined System of Direction Estimation and Sound Zooming of Multiple Speakers

This article presents a new system for estimation the direction of multiple speakers and zooming the sound of one of them at a time. The proposed system is a combination of two levels; namely, sound source direction estimation, and acoustic zooming. The sound source direction estimation uses so-called the energetic analysis method for estimation the direction of multiple speakers, whereas the acoustic zooming is based on modifying the parameters of the directional audio coding (DirAC) in order to zoom the sound of a selected speaker among the others. Both listening tests and objective assessments are performed to evaluate this system using different time-frequency transforms

Is General Relativity a simpler theory?

Gravity is understood as a geometrization of spacetime. But spacetime is also the manifold of the boundary values of the spinless point particle in a variational approach. Since all known matter, baryons, leptons and gauge bosons are spinning objects, it means that the manifold, which we call the kinematical space, where we play the game of the variational formalism of an elementary particle is greater than spacetime. This manifold for any mechanical system is a Finsler metric space such that the variational formalism can always be interpreted as a geodesic problem on this space. This manifold is just the flat Minkowski space for the free spinless particle. Any interaction modifies its flat Finsler metric as gravitation does. The same thing happens for the spinning objects but now the Finsler metric space has more dimensions and its metric is modified by any interaction, so that to reduce gravity to the modification only of the spacetime metric is to make a simpler theory, the gravitational theory of spinless matter. Even the usual assumption that the modification of the metric only involves dependence of the metric coefficients on the spacetime variables is also a restriction because in general these coefficients are dependent on the velocities. In the spirit of unification of all forces, gravity cannot produce, in principle, a different and simpler geometrization than any other interaction.Comment: 10 pages 1 figure, several Finsler metric examples and a conclusion section added. Minor correction

The Hamilton-Jacobi Formalism for Higher Order Field Theories

We extend the geometric Hamilton-Jacobi formalism for hamiltonian mechanics to higher order field theories with regular lagrangian density. We also investigate the dependence of the formalism on the lagrangian density in the class of those yelding the same Euler-Lagrange equations.Comment: 25 page

On Fermat's principle for causal curves in time oriented Finsler spacetimes

In this work, a version of Fermat's principle for causal curves with the same energy in time orientable Finsler spacetimes is proved. We calculate the secondvariation of the {\it time arrival functional} along a geodesic in terms of the index form associated with the Finsler spacetime Lagrangian. Then the character of the critical points of the time arrival functional is investigated and a Morse index theorem in the context of Finsler spacetime is presented.Comment: 20 pages, minor corrections, references adde

Converting Classical Theories to Quantum Theories by Solutions of the Hamilton-Jacobi Equation

By employing special solutions of the Hamilton-Jacobi equation and tools from lattice theories, we suggest an approach to convert classical theories to quantum theories for mechanics and field theories. Some nontrivial results are obtained for a gauge field and a fermion field. For a topologically massive gauge theory, we can obtain a first order Lagrangian with mass term. For the fermion field, in order to make our approach feasible, we supplement the conventional Lagrangian with a surface term. This surface term can also produce the massive term for the fermion.Comment: 30 pages, no figures, v2: discussions and references added, published version matche

Gauged Gravity via Spectral Asymptotics of non-Laplace type Operators

We construct invariant differential operators acting on sections of vector bundles of densities over a smooth manifold without using a Riemannian metric. The spectral invariants of such operators are invariant under both the diffeomorphisms and the gauge transformations and can be used to induce a new theory of gravitation. It can be viewed as a matrix generalization of Einstein general relativity that reproduces the standard Einstein theory in the weak deformation limit. Relations with various mathematical constructions such as Finsler geometry and Hodge-de Rham theory are discussed.Comment: Version accepted by J. High Energy Phys. Introduction and Discussion significantly expanded. References added and updated. (41 pages, LaTeX: JHEP3 class, no figures

Homogeneous variational problems: a minicourse

A Finsler geometry may be understood as a homogeneous variational problem, where the Finsler function is the Lagrangian. The extremals in Finsler geometry are curves, but in more general variational problems we might consider extremal submanifolds of dimension $m$. In this minicourse we discuss these problems from a geometric point of view.Comment: This paper is a written-up version of the major part of a minicourse given at the sixth Bilateral Workshop on Differential Geometry and its Applications, held in Ostrava in May 201

Energy-momentum conservation in pre-metric electrodynamics with magnetic charges

A necessary and sufficient condition for energy-momentum conservation is proved within a topological, pre-metric approach to classical electrodynamics including magnetic as well as electric charges. The extended Lorentz force, consisting of mutual actions by F=(E, B) on the electric current and G=(H, D) on the magnetic current, can be derived from an energy-momentum "potential" if and only if the constitutive relation G=G(F) satisfies a certain vanishing condition. The electric-magnetic reciprocity introduced by Hehl and Obukhov is seen to define a complex structure on the tensor product of 2-form pairs (F,G) which is independent of but consistent with the Hodge star operator defined by any Lorentzian metric. Contrary to a recent claim in the literature, it does not define a complex structure on the space of 2-forms itself.Comment: 8 pages, 1 fugur