Related papers: Hamilton-Jacobi formalism for Generalized Chaplygi…
In our previous papers [11,13] we showed that the Hamilton-Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. We also showed how…
Nonlocal gravity models are constructed to explain the current acceleration of the universe. These models are inspired by the infrared correction appearing in Einstein Hilbert action. Here we develop the Hamiltonian formalism of a nonlocal…
The multimomentum Hamiltonian formalism is applied to field systems represented by sections of composite manifolds $Y\to\Si\to X$ where sections of $\Si\to X$ are parameter fields, e.g., Higgs fields and gravitational fields. Their values…
We propose a new way to perform path integrals in quantum mechanics by using a quantum version of Hamilton-Jacobi theory. In classical mechanics, Hamilton-Jacobi theory is a powerful formalism, however, its utility is not explored in…
We consider two strongly hyperbolic Hamiltonian formulations of general relativity and their numerical integration with a free and a partially constrained symplectic integrator. In those formulations we use hyperbolic drivers for the shift…
In recent years it has been shown for hard sphere gas that, by retaining the correlation information, dynamical fluctuation and large deviation of empirical measure around Boltzmann equation could be proved, in addition to the classical…
Recently, M. de Le\'on el al. ([9]) have developed a geometric Hamilton-Jacobi theory for Classical Field Theories in the setting of multisymplectic geometry. Our purpose in the current paper is to establish the corresponding…
We use the formalism of geometrothermodynamics (GTD) to derive fundamental thermodynamic equations that are used to construct general relativistic cosmological models. In particular, we show that the simplest possible fundamental equation,…
We develop a technique for the reconstruction of the potential for a scalar field in cosmological models based on induced gravity. The potentials reproducing cosmological evolutions driven by barotropic perfect fluids, a cosmological…
In this work, results are presented of Hybrid-Monte-Carlo simulations of the tight-binding Hamiltonian of graphene, coupled to an instantaneous long-range two-body potential which is modeled by a Hubbard-Stratonovich auxiliary field. We…
We address the question of ambiguity in defining a Hamiltonian for a scalar field. We point out that the Hamiltonian for a real Klein-Gordon scalar field must be consistent with the energy density obtained from the Schrodinger equation in…
We construct the gauge invariant free action for cosmological perturbations for the nonminimally coupled inflaton field in the Jordan frame. For this the phase space formalism is used, which keeps track of all the dynamical and constraint…
On the basis of Hamilton a formalism the dynamic equations of movement scalar charged particles in a classical scalar field are formulated. Unlike earlier published works of the author the model with zero own weight of particles is…
In this paper, we propose a geometric Hamilton-Jacobi theory for systems of implicit differential equations. In particular, we are interested in implicit Hamiltonian systems, described in terms of Lagrangian submanifolds of $TT^*Q$…
In this work, we study the Friedmann-Robertson-Walker cosmology in which a Chaplygin gas is coupled to a non-linear scalar field in the framework of the Ho\v{r}ava-Lifshitz theory. In writing the action of the matter part, we use the…
In this work, we investigate the cosmological dynamics of a spatially flat Friedmann--Lema\^itre--Robertson--Walker Universe in the framework of generalized \( \mathcal{F}(\mathcal{R},\Sigma,\mathcal{T}) \) gravity by incorporating…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
In this work, we apply the formalism of dynamical systems to analyze the viability of the $\Lambda$CDM model in a generalized form of the hybrid metric-Palatini gravity theory written in terms of its dynamically equivalent scalar-tensor…
The Hamilton-Jacobi formalism generalized to 2-dimensional field theories according to Lepage's canonical framework is applied to several relativistic real scalar fields, e.g. massless and massive Klein-Gordon, Sinh and Sine-Gordon,…
Very recently, the Lee-Wick standard model has been introduced as a non-SUSY extension of the Standard model which solves the Hierarchy problem. In this model, each field kinetic term attains a higher derivative term. Like any Lee-Wick…