Related papers: Quantization from Hamilton-Jacobi theory with a ra…
D-dimensional constrained systems are studied with stochastic Lagrangian and\break Hamiltonian. It is shown that stochastic consistency conditions are second class constraints and Lagrange multiplier fields can be determined in…
We derive the Hamilton equations of motion for a constrained system in the form given by Dirac, by a limiting procedure, starting from the Lagrangean for an unconstrained system. We thereby ellucidate the role played by the primary…
The new scheme of stochastic quantization is proposed. This quantization procedure is equivalent to the deformation of an algebra of observables in the manner of deformation quantization with an imaginary deformation parameter (the Planck…
The fractional quantization of singular systems with second order Lagrangian is examined. The fractional singular Lagrangian is presented. The equations of motion are written as total differential equations within fractional calculus. Also,…
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
We propose an alternative to Dirac quantization for a quadratic constrained system. We show that this solves the Jacobi identity violation problem occuring in the Dirac quantization case and yields a well defined Fock space. By requiring…
Following the random approach of Mitake, Siconolfi,Tran and Yamada, we define a Lax--Oleinik formula adapted to evolutive weakly coupled systems of Hamilton--Jacobi equations. It is reminiscent of the corresponding scalar formula, with the…
Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology, such as the quantum bounce and…
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…
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and…
We show that within the Ashtekar formulation of General Relativity a considerably simple and compact form of the Lorentzian Hamiltonian constraint occurs for a particular value of the Barbero--Immirzi parameter.
Constrained optimization problems exist in many domains of science, such as thermodynamics, mechanics, economics, etc. These problems are classically solved with the help of the Lagrange multipliers and the Lagrangian function. However, the…
We introduce a single-channel opening in a random Hamiltonian and a quantized chaotic map: localization on the opening occurs as a sensible deviation of the wavefunction statistics from the predictions of random matrix theory, even in the…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
This paper is devoted to discrete mechanical systems subject to external forces. We introduce a discrete version of systems with Rayleigh-type forces, obtain the equations of motion and characterize the equivalence for these systems.…
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…
Systems invariant under the reparametrization of time were treated as constrained systems within Hamilton-Jacobi formalism. After imposing the integrability conditions the time-dependent Schr\"odinger equation was obtained. Three examples…
We develop Hamilton-Jacobi theory for Chaplygin systems, a certain class of nonholonomic mechanical systems with symmetries, using a technique called Hamiltonization, which transforms nonholonomic systems into Hamiltonian systems. We give a…
We introduce the notion of hidden quantum correlations. We present the mean values of observables depending on one classical random variable described by the probability distribution in the form of correlation functions of two (three, etc.)…
Starting from a Lagrangian we perform the full constraint analysis of the Hamiltonian for General relativity in the tetrad-connection formulation for an arbitrary value of the Immirzi parameter and solve the second class constraints,…