Related papers: Path Equations In Absolute Parallelism Space
Absolute Parallelism (AP) has many interesting features: large symmetry group of equations; field irreducibility with respect to this group; vast list of consistent second order equations not restricted to Lagrangian ones. There is the…
In this paper we elaborate on the symmetric teleparallel gravity (STPG) written in a non-Riemannian spacetime with nonzero nonmetricity, but zero torsion and zero curvature. Firstly we give a prescription for obtaining the nonmetricity from…
Compatible equations, Singularities of solutions, Topological charges and quasi-charges. PhD thesis (translated frorm Russian). The book shows the sights of Absolute Parallelism (AP), and contains useful information on the problem of…
Feynman's path integrals in ordinary, p-adic and adelic quantum mechanics are considered. The corresponding probability amplitudes $ K(x^{"},t^{"};x',t')$ for two-dimensional systems with quadratic Lagrangians are evaluated analytically and…
Using a geometry wider than Riemannian one, the parameterized absolute parallelism (PAP-) geometry, we derived a new curve containing two parameters. In the context of the geometrization philosophy, this new curve can be used as a…
Symmetries in the Lagrangian formalism of arbitrary order are analysed with the help of the so-called Anderson-Duchamp-Krupka equations. For the case of second order equations and a scalar field we establish a polynomial structure in the…
Two Lagrangian functions are used to construct geometric field theories. One of these Lagrangians depends on the curvature of space, while the other depends on curvature and torsion. It is shown that the theory constructed from the first…
In this paper we provide a \emph{global} investigation of the geometry of parallelizable manifolds (or absolute parallelism geometry) frequently used for application. We discuss the different linear connections and curvature tensors from a…
Given a smooth family of unparameterized curves such that through every point in every direction there passes exactly one curve, does there exist a Lagrangian with extremals being precisely this family? It is known that in dimension 2 the…
The paths on the {\bf R$^3$} real Euclidean manifold are defined as 2-dimensional simplicial strips; points are replaced by 2-simplexes and the orbits of the action of a one discrete-parameter group on the base manifold becomes a convex…
In this paper, we construct a field theory unifying gravity and electromagnetism in the context of Extended Absolute Parallelism (EAP-) geometry. This geometry combines, within its structure, the geometric richness of the tangent bundle and…
Contrary to previous approaches bringing together algebraic geometry and signatures of paths, we introduce a Zariski topology on the space of paths itself, and study path varieties consisting of all paths whose iterated-integrals signature…
We give here a covariant definition of the path integral formalism for the Lagrangian, which leaves a freedom to choose anyone of many possible quantum systems that correspond to the same classical limit without adding new potential terms…
Symmetries are essential for a consistent formulation of many quantum systems. In this paper we discuss a previously unnoticed symmetry, which is present for any Lagrangian term that involves $\dot{x}^2$. As a basic model that incorporates…
We study grassmannians associated with a linear space with a nondegenerate hermitian form. The geometry of these grassmannians allows us to explain the relation between a (pseudo-)riemannian projective geometry and the conformal structure…
Considering an extension of the principle of covarience to the action along a path in relativistic Lagrangian mechanics, we motivate the use of geometric -- i.e. covariant and parameter invariant -- Lagrangian functions. We then study some…
Closed systems in Newtonian mechanics obey the principle of Galilean relativity. However, the usual Lagrangian for Newtonian mechanics, formed from the difference of kinetic and potential energies, is not invariant under the full group of…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
Autoparallel curves along with geodesic curves can arise as trajectories of physical test bodies. We explicitly derive autoparallels as effective post-Riemannian geometric constructs, and at the same time we argue \emph{against} postulating…
Classical and quantum mechanics for an extended Heisenberg algebra with canonical commutation relations for position and momentum coordinates are considered. In this approach additional noncommutativity is removed from the algebra by linear…