Related papers: The Hamilton-Jacobi analysis for higher-order Cher…
Principles of successful Hamiltonian approaches, which were developed to describe free gravitational field(s) in the metric gravity, are formulated and discussed. By using the standard $\Gamma-\Gamma$ Lagrangian ${\cal L}_{\Gamma-\Gamma}$…
In this paper we extend the geometric formalism of Hamilton-Jacobi theory for Mechanics to the case of classical field theories in the k-symplectic framework.
We will analyze the constraint structure of the Einstein-Hilbert first-order action in two dimensions using the Hamilton-Jacobi approach. We will be able to find a set of involutive, as well as a set of non-involutive constraints. Using…
It is well known that a generic small perturbation of a Liouville-integrable Hamiltonian system causes breakup of resonant and near-resonant invariant tori. A general approach to the simple resonance case in the convex real-analytic setting…
A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of Covariant Quantum-Gravity (CQG-theory). The treatment is founded on the recently-identified Hamiltonian structure…
This article is dedicated to the proof of C^{\alpha} regularization effects of Hamilton- Jacobi equations. The proof is based on the De Giorgi method. The regularization is independent on the regularity of the Hamiltonian.
Found all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of…
The quantization method based on the quantum Hamiltonian Jacobi equation, is extended to two-dimensional non-separable but integrable Hamiltonians. It is shown that each wave function for those systems corresponds to a well-defined family…
In this paper, we apply the geometric Hamilton--Jacobi theory to obtain solutions of Hamiltonian systems in Classical Mechanics, that are either compatible with a cosymplectic or a contact structure. As it is well known, the first structure…
Hamilton-Jacobi theory is a fundamental subject of classical mechanics and has also an important role in the development of quantum mechanics. Its conceptual framework results from the advantages of transformation theory and, for this…
A generalised canonical formulation of gravity is devised for foliations of spacetime with codimension $n\ge1$. The new formalism retains n-dimensional covariance and is especially suited to 2+2 decompositions of spacetime. It is also…
We find the Holographic Renormalization Group equations for the holographic duals of generic gravity theories coupled to form fields and spin-1/2 fermions. Using Hamilton-Jacobi theory we discuss the structure of Ward identities, anomalies,…
Preliminary results toward the analysis of the Hamiltonian structure of multifield theories describing complex materials are mustered: we involve the invariance under the action of a general Lie group of the balance of substructural…
Higher dimensional Chern-Simons theories, even though constructed along the same topological pattern as in 2+1 dimensions, have been shown recently to have generically a non-vanishing number of degrees of freedom. In this paper, we carry…
Analytic energy bounds for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N(p_i^2 + m^2)^{1/2} - sum_{1=i<j}^N v/r_{ij}, with v>0, are derived by use of Jacobi relative coordinates. For gravity v=c/N,…
We apply the Kosambi-Cartan-Chern theory to perform an extensive examination of Jacobi stability of geodesics around rotating black hole solutions to dynamical Chern-Simons gravity, a theory that introduces modifications to General…
The gauge theory-formulation of string-motivated lineal gravity proposed by Cangemi and Jackiw is obtained by dimensional reduction from $(2+1)$ dimensional gravity with a Chern-Simons Lagrangian.
Examples of non-standard construction of Hamiltonian structures for dynamical systems and the respective Hamilton-Jacobi (H-J) equations, without using Lagrangians, are presented. Alternative H-J equations for Euler top are explicitly…
Fermions are coupled to the Einstein-Cartan system in the canonical formulation, including the cosmological, the Barbero-Immirzi, and the non-minimal coupling constants. The resulting ten first-class constraints generate gauge…
We argue that Hamilton-Jacobi equations provide a convenient and intuitive approach for studying the large-scale behavior of mean-field disordered systems. This point of view is illustrated on the problem of inference of a rank-one matrix.…