Related papers: Hamilton-Jacobi method for Domain Walls and Cosmol…
In this paper we constructed a semi-realistic cosmological model in a dynamic domain wall framework. Our universe is considered to be a (3+1) dimensional dynamic domain wall in a higher dimensional Einstein-Maxwell-Born-Infeld background.…
We present a theoretical analysis of the WDW approach to quantum cosmology extended to gravity theories with torsion. The dynamics of the FLRW universe is formulated as a classical Hamiltonian problem of point particle mechanics. Unlike in…
A fluid of domain walls has an effective equation of state $p_w = - {2/3}\rho_w$. This equation of state is qualitativelly in agreement with the supernova type Ia observations. We exploit a cosmological model where the matter content is…
We analyze the consistency of the ADM approach to KK model; we prove that KK reduction commute with ADM splitting. This leads to a well defined Hamiltonian; we provide the outcome. The electromagnetic constraint is derived from a…
In this paper, we review the discrete Hamilton--Jacobi theory from a geometric point of view. In the discrete realm, the usual geometric interpretation of the Hamilton--Jacobi theory in terms of vector fields is not straightforward. Here,…
The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the ambient of higher-order mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi…
Closed, spatially homogeneous cosmological models with a perfect fluid and a scalar field with exponential potential are investigated, using dynamical systems methods. First, we consider the closed Friedmann-Robertson-Walker models,…
We study stable homotopy through unstable methods applied to its representing infinite loop space, as pioneered by Curtis and Wellington. Using cohomology instead of homology, we find a width filtration whose subquotients are simple…
We study Euclidean Wilson loops at strong coupling using the AdS/CFT correspondence, where the problem is mapped to finding the area of minimal surfaces in Hyperbolic space. We use a formalism introduced recently by Kruczenski to…
We show that the spacetimes of domain wall solutions to the coupled Einstein-scalar field equations with a given scalar field potential fall into two classes, depending on whether or not reflection symmetry on the wall is imposed. Solutions…
We introduce a new method for analyzing nonlinear wave-Klein-Gordon systems and establishing global-in-time existence results for the Cauchy problem when the initial data need not have compact support. This method, which we call the…
In a stationary case and for any potential, we solve the three-dimensional quantum Hamilton-Jacobi equation in terms of the solutions of the corresponding Schrodinger equation. Then, in the case of separated variables, by requiring that the…
We consider a scenario where our universe is taken as a three-dimensional domain wall embedded in a five-dimensional Minkowski space-time, as originally proposed by Brito and collaborators [1]. We explore the existence of a richer class of…
The paper is devoted to the Hamiltonian treatment of classical and quantum properties of Liouville field theory on a timelike strip in 2d Minkowski space. We give a complete description of classical solutions regular in the interior of the…
The Hamilton-Jacobi formalism for a geodetic brane-like universe described by the Regge-Teitelboim model is developed. We focus on the description of the complete set of Hamiltonians that ensure the integrability of the model in addition to…
This is a short review of a series of papers which, in collaboration with Yue Ma, establish several novel existence results for systems of coupled wave-Klein-Gordon equation. Our method, the Hyperbolic Hyperboloidal Method, has allowed us…
Domain walls are topological defects that may have formed in the early Universe through the spontaneous breakdown of discrete symmetries, and can be a strong source of gravitational waves (GWs). We perform 3D lattice field theory…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion for three singular systems are obtained as total differential equations in many variables. The integrability conditions for these syatems lead us to the…
Superpotentials in ${\cal N}=2$ supersymmetric classical mechanics are no more than the Hamilton characteristic function of the Hamilton-Jacobi theory for the associated purely bosonic dynamical system. Modulo a global sign, there are…
Domain walls, arising from the spontaneous breaking of a discrete symmetry, can be coupled to charge carriers. In much the same way as the Witten model for superconducting cosmic string, an investigation is made here in the case of…