Related papers: Hamilton-Jacobi Method and Gravitation
Semiclassical methods are essential in analyzing quantum mechanical systems. Although they generally produce approximate results, relatively rare potentials exist for which these methods are exact. Such intriguing potentials serve as…
Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket…
In this paper we extend the geometric formalism of the Hamilton-Jacobi theory for time dependent Mechanics to the case of classical field theories in the k-cosymplectic framework.
A method has been recently proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example a version of quantized space-time is considered here. It is found that there is a…
The literature on quantum-gravity-inspired scenarios for the quantization of spacetime has so far focused on particle-physics-like studies. This is partly justified by the present limitations of our understanding of quantum-gravity…
Recently, we have suggested some semi-quantitative Hamiltonian for an electron in a hydrogen atom in a weak gravitational field, which takes into account quantum effects of electron motion in the atom. We have shown that this Hamiltonian…
Semiclassical techniques have proven to be a very powerful method to extract physical effects from different quantum theories. Therefore, it is expected that in the near future they will play a very prominent role in the context of quantum…
We present the analytic solution for the stationary quantum HamiltonJacobi equation. Knowing the strong relation between the Riccati and quantum Hamilton-Jacobi equations, we develop a simple method to obtain the exact solution. Then, in…
In many physical problems it is not possible to find an exact solution. However, when some parameter in the problem is small, one can obtain an approximate solution by expanding in this parameter. This is the basis of perturbative methods,…
We discuss Hamiltonian learning in quantum field theories as a protocol for systematically extracting the operator content and coupling constants of effective field theory Hamiltonians from experimental data. Learning the Hamiltonian for…
We propose a method to recover the time variable and the classical evolution of the Universe from the minisuperspace wave function of the Wheeler-DeWitt equation. Defining a Hamilton-Jacobi characteristic function $W$ as the imaginary part…
Semi-classical gravity attempts to define a hybrid theory in which a classical gravitational field is coupled to a unitarily evolving quantum state. Although semi-classical gravity is inconsistent with observation, a viable theory of this…
Methods for measuring an integral of a classical field via local interaction of classical bits or local interaction of qubits passing through the field one at a time are analyzed. A quantum method, which has an exponentially better…
When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, the…
We develop a semiclassical framework for studying quantum particles constrained to curved surfaces using the momentous quantum mechanics formalism, which extends classical phase-space to include quantum fluctuation variables (moments). In a…
Reduction theory has played a major role in the study of Hamiltonian systems. On the other hand, the Hamilton-Jacobi theory is one of the main tools to integrate the dynamics of certain Hamiltonian problems and a topic of research on its…
How the time evolution which is typical for classical cosmology emerges from quantum cosmology? The answer is not trivial because the Wheeler-DeWitt equation is time independent. A framework associating the quantum Hamilton-Jacobi to the…
We generalise Langlois' Hamiltonian treatment of gauge-invariant linear cosmological perturbations to a cosmological setting with multiple scalar fields minimally coupled to gravity. We review the Hamilton-Jacobi-like technique for a…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
Witnessing non-classicality in the gravitational field has been claimed to be practically impossible. This constitutes a deep problem, which has even lead some researchers to question whether gravity should be quantised, due to the weakness…