相关论文: Generalized Hamilton Function in the Phase Space o…

An exact description of the statistical motion of active particles in three dimension is presented in the framework of a generalized diffusion equation. Such a generalization contemplates a non-local, in time and space, connecting (memory)…

The generalized harmonic equations of general relativity are written in 3+1 form. The result is a system of partial differential equations with first order time and second order space derivatives for the spatial metric, extrinsic curvature,…

We examine vacuum fluctuations in theories with modified dispersion relations which represent dimensional reduction at high energies. By changing units of energy and momentum we can obtain a description rendering the dispersion relations…

We consider a Hamiltonian system of particles, interacting through of a smooth pair potential. We look at the system on a space scale of order {\epsilon}^1, times of order {\epsilon}^2, and mean velocities of order {\epsilon}, with…

We consider spaces of trial wavefunctions for ground states and edge excitations in the fractional quantum Hall effect that can be obtained in various ways. In one way, functions are obtained by analyzing the entanglement of the ground…

The curvature of the inertial or gravitational potentials defined as a Hodge-Helmholtz decomposition of acceleration into an irrotational and a solenoidal components, enable to federate certain domains of macroscopic physics. After two…

Basic principles of the Hamilton approach developed for the metric General Relativity (Einstein`s GR) are discussed. In particular, we derive the Hamiltonian of the metric GR in the explicit form. This Hamiltonian is a quadratic function of…

In an earlier work we showed that the gravitational interaction could be reproduced as a retarded dispersion interaction (Casimir interaction) between particles composed of hypothetical particles having harmonic oscillator interactions.…

Gravity, and the puzzle regarding its energy, can be understood from a gauge theory perspective. Gravity, i.e., dynamical spacetime geometry, can be considered as a local gauge theory of the symmetry group of Minkowski spacetime: the…

A unified form for real and complex wave functions is proposed for the stationary case, and the quantum Hamilton-Jacobi equation is derived in the three-dimensional space. The difficulties which appear in Bohm's theory like the vanishing…

A large population of extended substructures generates a stochastic gravitational field that is fully specified by the function $p({\bf F})$, which defines the probability that a tracer particle experiences a force $\bf F$ within the…

Phase space of General Relativity is extended to a Poisson manifold by inclusion of the determinant of the metric and conjugate momentum as additional independent variables. As a result, the action and the constraints take a polynomial…

Hamilton's principle is extended to have compatible initial conditions to the strong form. To use a number of computational and theoretical benefits for dynamical systems, the mixed variational formulation is preferred in the systems other…

We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d…

We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…

Integration over connection type variables in the path integral for the discrete form of the first order formulation of general relativity theory is studied. The result (a generalized function of the rest of variables of the type of tetrad…

The regularized vacuum fluctuation related to a conformally coupled massless scalar field defined on a space-time with dynamical horizon is computed with respect a radially moving observer in a generic flat Friedmann-Robertson-Walker…

We consider a class of finite-dimensional dynamical systems whose equations of motion are derived from a non-local-in-time action principle. The action functional has a zeroth order piece derived from a local Hamiltonian and a perturbation…

The small angle approximation often fails to explain experimental data, does not even predict if a plane pendulum's period increases or decreases with increasing amplitude. We make a perturbation ansatz for the Conserved Energy Surfaces of…

We construct Hamiltonian Floer complexes associated to continuous, and even lower semi-continuous, time dependent exhaustion functions on geometrically bounded symplectic manifolds. We further construct functorial continuation maps…