Related papers: On Hamilton-Jacobi theory: its geometry and relati…
In this article we provide a Hamilton-Jacobi formalism in locally conformally symplectic manifolds. Our interest in the Hamilton-Jacobi theory comes from the suitability of this theory as an integration method for dynamical systems, whilst…
We discuss the Hamilton-Jacobi approach for a constrained system. We obtain the equation of motion for a singular system as total differential equations in many variables. We investigate the integrability conditions without using any gauge…
The Hamiltonian description of the self-consistent interaction between an electromagnetic plane-wave and a co-propagating beam of charged particles is considered. We show how the motion can be reduced to a one-dimensional Hamiltonian model…
In this work we study the theory of linearized gravity via the Hamilton-Jacobi formalism. We make a brief review of this theory and its Lagrangian description, as well as a review of the Hamilton-Jacobi approach for singular systems. Then…
The additional information within a Hamilton-Jacobi representation of quantum mechanics is extra, in general, to the Schr\"odinger representation. This additional information specifies the microstate of $\psi$ that is incorporated into the…
By using the Hamilton-Jacobi [HJ] framework the three dimensional Palatini theory plus a Chern-Simons term [PCS] is analyzed. We report the complete set of $HJ$ Hamiltonians and a generalized $HJ$ differential from which all symmetries of…
The algebraic-geometric approach is extended to study solutions of N-component systems associated with the energy dependent Schrodinger operators having potentials with poles in the spectral parameter, in connection with Hamiltonian flows…
In this paper we revise the main aspects of the Hamiltonian analogy: the fact that optical paths are completely analogous to mechanical trajectories. We follow Schr\"{o}dinger's original idea and go beyond this analogy by changing over from…
In this paper, we start with the quantum Hamilton-Jacobi approach and show that the underlying complex pole evolution of the Schr\"odinger equation is described by the quantum action in terms of a random matrix. The wave function is given…
Interference dynamics is analyzed in the light of the complex quantum Hamilton-Jacobi formalism, using as a working model the collision of two Gaussian wave packets. Though simple, this model nicely shows that interference in quantum…
This paper presents a concise review of the quantum tunneling approach to Hawking radiation, covering its theoretical foundations, extensions, and experimental efforts. We begin by outlining the Hamilton-Jacobi and Parikh-Wilczek methods,…
In curved space-time, Hamilton-Jacobi equation is a semi-classical particle's motion equation, which plays an important role in the research of black hole physics. In this paper, starting from Dirac equation describing the spin 1/2 fermion…
The relation that exists in quantum mechanics among action variables, angle variables and the phases of quantum states is clarified, by referring to the system of a generalized oscillator. As a by-product, quantum-mechanical meaning of the…
A simple method to deal with four dimensional Hamilton-Jacobi equation for null hypersurfaces is introduced. This method allows to find simple geometrical conditions which give rise to the failure of the WKB approximation on curved…
This is a survey article, from the viewpoint of the completeness of the Marsden- Weinstein reduction, to introduce briefly some recent developments of the symmetric reductions and Hamilton-Jacobi theory of the regular controlled Hamiltonian…
In this paper, we discuss how the concepts of Hamiltonian optics are internally connected to the scalar wave theory of light rays. It is shown that the solutions of the reduced wave equation are similar to Huygen's wavelets, and they can be…
Quantum Hamilton-Jacobi quantization scheme uses the singularity structure of the potential of a quantum mechanical system to generate its eigenspectrum and eigenfunctions, and its efficacy has been demonstrated for several well known…
The paper is devoted to prove the existence of a local solution of the Hamilton-Jacobi equation in field theory, whence the general solution of the field equations can be obtained. The solution is adapted to the choice of the submanifold…
This survey examines separation of variables for algebraically integrable Hamiltonian systems whose tori are Jacobians of Riemann surfaces. For these cases there is a natural class of systems which admit separations in a nice geometric…
In this note we discuss the invariance under general changes of reference frame of all the physical predictions of particle detector models in quantum field theory in general and, in particular, of those used in quantum optics to model…