Related papers: Geodesic deviation to all orders via a tangent bun…
We study incommensurate fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives and generalized fractional integrals and derivatives. We obtain necessary optimality…
A conformal structure on a manifold $M^n$ induces natural second order conformally invariant operators, called M\"obius and Laplace structures, acting on specific weight bundles of $M$, provided that $n\ge 3$. By extending the notions of…
It is proved that the set of geodesic circles in two dimensions may be given a variational description and the explicit form of it is presented. In the limit case of the Euclidean geometry a certain claim of uniqueness of such description…
We pose a new algebraic formalism for studying differential calculus in vector bundles. This is achieved by studying various functors of differential calculus over arbitrary graded commutative algebras (DCGCA) and applying this language to…
We consider the problem of covariant gauge-fixing in the most general setting of the field-antifield formalism, where the action W and the gauge-fixing part X enter symmetrically and both satisfy the Quantum Master Equation. Analogous to…
We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the…
We give a definition of `coherent tangent bundles', which is an intrinsic formulation of wave fronts. In our application of coherent tangent bundles for wave fronts, the first fundamental forms and the third fundamental forms are considered…
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…
A set of linear second-order differential equations is converted into a semigroup, whose algebraic structure is used to generate many novel equations. Two independent methods that can be used to derive the equations of the semigroup are…
We define formal exponential maps for any graded manifold as maps from the formal tangent bundle (that we also define) into the graded manifold. We show that each such map uniquely determines and is determined by its associated Grothendieck…
It is shown that any second order dynamic equation on a configuration bundle $Q\to R$ of non-relativistic mechanics is equivalent to a geodesic equation with respect to a (non-linear) connection on the tangent bundle $TQ\to Q$. The case of…
Quadratic Lagrangians are introduced adding surface terms to a free particle Lagrangian. Geodesic equations are used in the context of the Hamilton-Jacobi formulation of constrained sysytem. Manifold structure induced by the quadratic…
We revisit the gauge-covariant canonical formalism by separating explicitly physical and gauge degrees of freedom. We show in particular that the gauge-invariant linear and angular momentum operators proposed by Chen et al. can consistently…
The theory of gauge fields in Theoretical Physics poses several mathematical problems of interest in Differential Geometry and in Field Theory. Below we tackle one of these problems: The existence of a finite system of generators of…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
The geodesic complexity of a Riemannian manifold is a numerical isometry invariant that is determined by the structure of its cut loci. In this article we study decompositions of cut loci over whose components the tangent cut loci fiber in…
We give a systematic and self-contained account of the construction of geometrically decomposed bases and degrees of freedom in finite element exterior calculus. In particular, we elaborate upon a previously overlooked basis for one of the…
A new perspective on the classical mechanical formulation of particle trajectories in lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant Lagrangian…