Related papers: Hamilton--Jacobi meet M\"obius
We investigate the kinetics of a nonrelativistic particle interacting with a constant external force on a Lie-algebraic noncommutative space. The structure constants of a Lie algebra, also called noncommutative parameters, are constrained…
PT-symmetric quantum mechanics is an alternative formulation of quantum mechanics in which the mathematical axiom of Hermiticity (transpose and complex conjugate) is replaced by the physically transparent condition of space-time reflection…
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…
Recently we showed that the postulated diffeomorphic equivalence of states implies quantum mechanics. This approach takes the canonical variables to be dependent by the relation p=\partial_q S_0 and exploits a basic GL(2,C)-symmetry which…
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…
In this work we discuss the natural appearance of the Generalized Brackets in systems with non-involutive (equivalent to second class) constraints in the Hamilton-Jacobi formalism. We show how a consistent geometric interpretation of the…
A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…
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 present exact energy spectrum and eigenfunctions of the one-dimensional hydrogen atom in the presence of the minimal length uncertainty. By requiring the self-adjointness property of the Hamiltonian, we completely determine the…
In most introductory courses on quantum mechanics one is taught that the Hamiltonian operator must be Hermitian in order that the energy levels be real and that the theory be unitary (probability conserving). To express the Hermiticity of a…
The quantization of the gravitational field is discussed within the exact uncertainty approach. The method may be described as a Hamilton-Jacobi quantization of gravity. It differs from previous approaches that take the classical…
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…
By adding an extra Hilbert space to Hadamard Quantum Walk on Cycles (QWC), we presented a new type of QWCs called M\"obius Quantum Walk (MQW). The new space configuration enables the particle to rotate around the axis of movement. We…
With approaching quantum/noncommutative models for the deep microscopic spacetime in mind, and inspired by our recent picture of the (projective) Hilbert space as the model of physical space behind basic quantum mechanics, we reformulate…
In this paper, we sketch and emphasize the automatic emergence of a quantum potential (QP) in general Hamilton-Jacobi equation via commuting relations, quantum canonical transformations and without the straight effect of wave function. The…
The indeterministic character of physical laws is generally considered to be the most important consequence of quantum physics. A deterministic point of view, however, together with the possibility of well defined Hamiltonian trajectories,…
By means of numerical solutions of the quantum Hamilton Jacobi equation, a general WKB-like representation for one-dimensional wave functions is obtained. This representation is unique in the classically forbidden regions, while in the…
Considering quantum cosmological minisuperspace models with positive potential, we present evidence that (i) despite common belief there are perspectives for defining a unique, naturally preferred decomposition of the space H of wave…
A rigorous \textit{ab initio} derivation of the (square of) Dirac's equation for a single particle with spin is presented. The general Hamilton-Jacobi equation for the particle expressed in terms of a background Weyl's conformal geometry is…
Consistent dynamics which couples classical and quantum degrees of freedom exists, provided it is stochastic. This dynamics is linear in the hybrid state, completely positive and trace preserving. One application of this is to study the…