Related papers: Morse theory in path space

Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of geometric properties of smooth manifolds. Round fold maps were introduced as stable fold maps…

We try to obtain meromorphic solution of Time dependent Schroedinger equation which partially satisfies Painleve Integrable property. Our study and analysis exhibits meromorphic behavior of classical particle trajectory. In other words,…

Many moduli spaces are constructed as quotients of group actions; this paper surveys the classical theory, as well as recent progress and applications. We review geometric invariant theory for reductive groups and how it is used to…

By considering a spatial curve in a Euclidean space, we use its components, together with attaining a cyclic matrix, to show that this matrix is homothetic too and is in correspondence with a homothetic motion. Furthermore, if the curve…

By using asymptotic Morse inequalities we give a lower bound for the space of holomorphic sections of high tensor powers in a positive line bundle over a q-concave domain. The curvature of the positive bundle induces a hermitian metric on…

We construct a relativistic and curved space version of action- angle variables for a particle trapped in a gravity and electromagnetic background with time-like isometry. As an example, we consider a particle in AdS background.…

We analyse the motion of the spinning body (in the pole-dipole approximation) in the gravitational and electromagnetic fields described by the Mathisson-Papapetrou-Dixon-Souriau equations. First, we define a novel spin condition for the…

The geometrical representation of the path integral reduction Jacobian obtained in the problem of the path integral quantization of a scalar particle motion on a smooth compact Riemannian manifold with the given free isometric action of the…

In this paper, as a fundamental study on the theory of Morse functions and their higher dimensional versions or fold maps and applications to geometric theory of manifolds, which were started in 1950s by differential topologists such as…

The motion of charged particles in spacetimes containing a submanifold of constant positive or negative curvature is considered, with the electromagnetic tensor proportional to the volume two-form form of the submanifold. In the positive…

We introduce an algebraic system which can be used as a model for spaces with geodesic paths between any two of their points. This new algebraic structure is based on the notion of mobility algebra which has recently been introduced as a…

The studies of influence of spin on a photon's motion in a Schwartzschild spacetime is continued. In the previous paper [13] the first order correction to the geodesic motion is found for the first half of the photon world line. The system…

We derive an action for scalar quantum field theory with cubic interaction in the context of relative locality. Beginning with the generating functional for standard $\varphi^3$--theory and the corresponding Feynman rules we modify them to…

A Morse 2-function is a generic smooth map from a manifold M of arbitrary finite dimension to a surface B. Its critical set maps to an immersed collection of cusped arcs in B. The aim of this paper is to explain exactly when it is possible…

A Jacobi field on a Riemannian manifold M is defined along a geodesic. We generalize this notion to an arbitrary smooth curve, and call it an infinitesimal isometry along the curve. We give two approaches to this: 1) compute the complete…

Physical path integral formulation of motion of particles in Riemannian spaces is outlined and extended to deduce the corresponding field theoretical formulation. For the special case of a zero rest mass particle in Minkowski manifold, it…

In this paper we review some aspects of relativistic particles' mechanics in the case of a non-trivial geometry of momentum space. We start with showing how the curved momentum space arises in the theory of gravity in 2+1 dimensions coupled…

In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a non-trivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are…

This paper presents a new approach to phase space trajectories in quantum mechanics. A Moyal description of quantum theory is used, where observables and states are treated as classical functions on a classical phase space. A quantum…

We investigate the behaviour of a particle moving on the quotient manifold $M=C^2/Z_$ which is derived from the EH metric as the two centers approach each other. In the classical region of the configuration space we specify the physically…