Related papers: Revisiting Legendre transformations in Finsler geo…
After surveying the quantum kinematics and dynamics of statistical transmutation, I show how this concept suggests a phase diagram for the two-dimensional matter in a magnetic field, as a function of quantum statistics. I discuss the…
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified…
Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…
We consider transformation maps on the space of states which are symmetries in the sense of Wigner. Due to the convex nature of the space of states, the set of these maps has a convex structure. We investigate the possibility of a complete…
We review the current status of Finsler-Lagrange geometry and generalizations. The goal is to aid non-experts on Finsler spaces, but physicists and geometers skilled in general relativity and particle theories, to understand the crucial…
We translate Penrose's singularity theorem to a Finsler spacetime. To that end, causal concepts in Lorentzian geometry are extended, including definitions and properties of focal points and trapped surfaces, with careful attention paid to…
For Legendre curves, we consider surfaces of revolution of frontals. The surface of revolution of a frontal can be considered as a framed base surface. We give the curvatures and basic invariants for surfaces of revolution by using the…
We study the geometrical background of the Hamiltonian formalism of first-order Classical Field Theories. In particular, different proposals of multimomentum bundles existing in the usual literature (including their canonical structures)…
Recently, classical results on completeness of trajectories of Hamiltonian systems obtained at the beginning of the seventies, have been revisited, improved and applied to Lorentzian Geometry. Our aim here is threefold: to give explicit…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
Physical foundations for relativistic spacetimes are revisited, in order to check at what extent Finsler spacetimes lie in their framework. Arguments based on inertial observers (as in the foundations of Special Relativity and Classical…
The Legendre transform expresses dynamics of a classical system through first-order Hamiltonian equations. We consider coherent state transforms with a similar effect in quantum mechanics: they reduce certain quantum Hamiltonians to…
Berwald geometries are Finsler geometries close to (pseudo)-Riemannian geometries. We establish a simple first order partial differential equation as necessary and sufficient condition, which a given Finsler Lagrangian has to satisfy to be…
We discuss the most general Finsler spacetime geometry obeying the cosmological symmetry group $\mathrm{SO}(4)$. On this background geometry we derive the equations of motion for the most general kinetic fluid obeying the same cosmological…
We present the basic formulation of Hamilton dynamics in complex phase space. We extend the Hamilton's function by including the imaginary part and find out the corresponding Hamilton's canonical equation of motion. Example of simple…
We review recent developments in cosmological models based on Finsler geometry and extensions of general relativity within this framework. Finsler geometry generalizes Riemannian geometry by allowing the metric tensor to depend on position…
We find that, in presence of the Snyder geometry, the notion of translational invariance needs to be modified, allowing a momentum dependence of this symmetry. This step is necessary to build the maximally localized states and the Feynman…
Considering a Hamiltonian Dynamical System describing the motion of charged particle in a Tokamak or a Stellarator, we build a change of coordinates to reduce its dimension. This change of coordinates is in fact an intricate succession of…
We consider the geometry of spacetime based on a non-metric, Finslerian, length measure, which, in terms of physics, represents a generalized clock. Our defnition of Finsler spacetimes ensure a well defined notion of causality, a precise…
Special class of Finsler metrics that can be decomposed to the product of two Riemannian metrics is considered. Based on such decomposition a new kind of Finsler gravity is suggested. Physical applications of Finsler decomposed metric are…