Related papers: Revisiting Legendre transformations in Finsler geo…
A non-symplectic generalization of Hamiltonian mechanics is considered. It allows include into consideration "non-Lagrange" systems, such as theory of charged particle in the field of magnetic monopole. The corresponding generalization for…
The application of the Legendre transformation to a hyperregular Lagrangian system results in a Hamiltonian vector field generated by a Hamiltonian defined on the phase space of the mechanical system. The Legendre transformation in its…
In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of $k$-cosymplectic geometry. We discuss the relation between Lagrangian and Hamiltonian…
Quantum particles under geometric constraints are sensitive to the geometry and topology of the underlying space. We analytically study the laser-driven nonlinear dynamics of a quantum particle whose motion is constrained to a…
The Finsler-relativistic metric function $F(g;R)$ and the associated Hamiltonian function $H(g;P)$, being considered together with explicit Finslerian special-relativistic kinematic transformations, give rise to a self-consistent and…
Applying the cosmological principle to Finsler spacetimes, we identify the Lie Algebra of symmetry generators of spatially homogeneous and isotropic Finsler geometries, thus generalising Friedmann-Lema\^{i}tre-Robertson-Walker geometry. In…
The task of finding a consistent relationship between a quantum Hamiltonian and a classical Lagrangian is of utmost importance for basic, but ubiquitous techniques like canonical quantization and path integrals. Nonconvex kinetic energies…
A new definition for the path integral is proposed in terms of Finsler geometry. The conventional Feynman's scheme for quantisation by Lagrangian formalism suffers problems due to the lack of geometrical structure of the configuration space…
Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities…
We investigate the gravitational field of a kinetic gas beyond its usual derivation from the second moment of the one-particle distribution function (1PDF), that serves as energy-momentum tensor in the Einstein equations. This standard…
For the general class of pseudo-Finsler spaces with $(\alpha,\beta)$-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means that the fundamental tensor has Lorentzian…
We study underlying geometric structures for integral variational functionals, depending on submanifolds of a given manifold. Applications include (first order) variational functionals of Finsler and areal geometries with integrand the…
We introduce a class of $n$-dimensional (possibly inhomogeneous) spin-like lattice systems presenting modulated phases with possibly different textures. Such systems can be parameterized according to the number of ground states, and can be…
An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum…
We present a study of geometric phases in classical wave and polarisation optics using the basic mathematical framework of quantum mechanics. Important physical situations taken from scalar wave optics, pure polarisation optics, and the…
The differential geometric aspects of Geometric Phases are reviewed.
Relations between kinematics, geometry and law of reference frame motion are considered. We show, that kinematical tensors define geometry up to a space functional arbitrariness when integrability condition for spin tensor is satisfied.…
In this paper, we first provide an updated survey of the geometry of complex Cartan spaces. New characterizations for some particular classes of complex Cartan spaces are pointed out, e.g. Landsberg-Cartan, strongly Berwald-Cartan and…
Lorentz invariance is one of the foundations of modern physics; however, Lorentz violation may happen from the perspective of quantum gravity, and plenty of studies on Lorentz violation have arisen in recent years. As a good tool to explore…
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…