Related papers: Quantum Mechanics on Curved Hypersurfaces
We first generalise the standard Wigner function to Dirac fermions in curved spacetimes. Secondly, we turn to the Moyal quantisation of systems with constraints. Gravity is used as an example.
The relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of Hamiltonian systems having no gauge conditions. It is traced out that the two quantization methods may give…
The complex unit appearing in the equations of quantum mechanics is generalised to a quaternionic structure on spacetime, leading to the consideration of complex quantum mechanical particles whose dynamical behaviour is governed by…
One of the central difficulties in the quantization of the gravitational interactions is that they are described by a set of constraints. The standard strategy for dealing with the problem is the Dirac quantization procedure, which leads to…
Geometric momentum is the appropriate momentum for a particle constrained to move on a curved surface, which depends on the extrinsic curvature and leads to observable effects, and curvature-induced quantum potentials appear for a…
An elementary introduction is provided to the phase space quantization method of Moyal and Wigner. We generalize the method so that it applies to 2-dimensional surfaces, where it has an interesting connection with quantum holography. In the…
We provide a unique and novel extension of da Costa's calculation of a quantum mechanically constrained particle. This is achieved by analyzing the perturbative back reaction of the quantum confined particle's eigenstates and spectra upon…
We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so…
These are introductory notes on the study of the Dirac equation in curved spacetime and its relation to hidden symmetries of the dynamics. We present general results on the relation between special spacetime tensors and hidden symmetries,…
We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. First, we study the…
Within the quark model and hyperspherical method, the bound states of four heavy quarks and antiquarks (tetraquarks) are investigated. In hyperradial approximation, the Schroedinger equation is reduced to a one-dimensional equation after…
The diffeomorphism symmetry of general relativity leads in the canonical formulation to constraints, which encode the dynamics of the theory. These constraints satisfy a complicated algebra, known as Dirac's hypersurface deformation…
The restriction problem is better understood for hypersurfaces and recent progresses have been made by bilinear and multilinear approaches and most recently polynomial partitioning method which is combined with those estimates. However, for…
Exact procedures that follow Dirac's constraint quantization of gauge theories are usually technically involved and often difficult to implement in practice. We overview an "effective" scheme for obtaining the leading order semiclassical…
We examine two singular Lagrangian systems with constraints which apparently reduce the phase space to a 2-dimensional sphere and a 2-dimensional hyperboloid. Rigorous constraint analysis by Dirac's method, however, gives 2-dimensional open…
We write the Dirac equation in curved 4-dimensional Lorentzian spacetime using concepts from the analysis of partial differential equations as opposed to geometric concepts.
The goal of this paper is to propose and discuss a practical way to implement the Dirac algorithm for constrained field models defined on spatial regions with boundaries. Our method is inspired in the geometric viewpoint developed by Gotay,…
This thesis is devoted to the Differential Geometry of curves and surfaces along with applications in Quantum Mechanics. In the 1st part we introduce the well known Frenet frame. Later, we show that the curvature function is a lower bound…
A new framework for deriving equations of motion for constrained quantum systems is introduced, and a procedure for its implementation is outlined. In special cases the framework reduces to a quantum analogue of the Dirac theory of…
Alternative versions of the Klein-Gordon and Dirac equations in a curved spacetime are got by applying directly the classical-quantum correspondence.