Related papers: Quantum particle on hyperboloid
A canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or, Hamiltonian) constraint. Using the new canonical coordinates, it is then easy to obtain explicit…
We present here the canonical treatment of spherically symmetric (quantum) gravity coupled to spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the reduced phase space which is…
Assuming equation of state for quintessential matter: $p=w(z)\rho$, we analyse dynamical behaviour of the scale factor in FRW cosmologies. It is shown that its dynamics is formally equivalent to that of a classical particle under the action…
The advent of hybrid computing platforms consisting of quantum processing units integrated with conventional high-performance computing brings new opportunities for algorithm design. By strategically offloading select portions of the…
We study time-like hypersurfaces with vanishing mean curvature in the (3+1) dimensional Minkowski space, which are the hyperbolic counterparts to minimal embeddings of Riemannian manifolds. The catenoid is a stationary solution of the…
The Hilbert space of a free massless particle moving on a group manifold is studied in details using canonical quantisation. While the simplest model is invariant under a global symmetry, $G \times G$, there is a very natural way to…
We investigate the parameter dynamics of eigenvalues of Hamiltonians ('level dynamics') defined on symmetric spaces relevant for condensed matter and particle physics. In particular we: 1) identify appropriate reduced manifold on which the…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
The effective classical/quantum dynamics of a particle constrained on a closed line embedded in a higher dimensional configuration space is analyzed. By considering explicit examples it is shown how different reduction mechanisms produce…
In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical…
Quantum-mechanical wave equation for a particle with spin 1 is investigated in presence of external magnetic field in spaces with non-Euclidean geometry with constant positive curvature. Separation of the variable is performed; differential…
A simple one dimensional model is introduced describing a two particle "atom" approaching a point at which the interaction between the particles is lost. The wave function is obtained analytically and analyzed to display the entangled…
The operator and the functional formulations of the dynamics of constrained systems are explored for determining unambiguously the quantum Hamiltonian of a nonrelativistic particle in a curved space.
We review the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analyse the information contained in the solutions of the Wheeler-DeWitt equation and…
We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…
Some recent results concerning a particle confined in a one-dimensional box with moving walls are briefly reviewed. By exploiting the same techniques used for the 1D problem, we investigate the behavior of a quantum particle confined in a…
We revise the problem of the quantization of relativistic particle, presenting a modified consistent canonical scheme, which allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quantization…
It is possible that relativistic symmetries become deformed in the semiclassical regime of quantum gravity. Mathematically, such deformations lead to the noncommutativity of spacetime geometry and non-vanishing curvature of momentum space.…
Using the concept of real tunneling configurations (classical signature change) and nucleation energy, we explore the consequences of an alternative minimization procedure for the Euclidean action in multiple-dimensional quantum cosmology.…
We perform the momentum-space quantization of a spin-less particle moving on the $SU(2)$ group manifold, that is, the three-dimensional sphere $S^{3}$, by using a non-canonical method entirely based on symmetry grounds. To achieve this…