Related papers: Quantum Mechanics on Curved Hypersurfaces
We use an exact solution of the elastic membrane shape equation, representing the curvature, which will serve as a quantum potential in the quantum mechanical two dimensional Schrodinger equation for a (quasi-) particle on the surface of…
Starting from the QCD Lagrangian and taking into account both perturbative and nonperturbative effects, we use the method of vacuum correlators to derive the Dirac equation (rigorously for the Coulomb interaction and heuristically for the…
We give new estimates for the eigenvalues of the hypersurface Dirac operator in terms of the intrinsic energy-momentum tensor, the mean curvature and the scalar curvature. We also discuss their limiting cases as well as the limiting cases…
The experimental techniques have evolved to a stage where various examples of nanostructures with non-trivial shapes have been synthesized, turning the dynamics of a constrained particle and the link with geometry into a realistic and…
We investigate the general properties of the dimensional reduction of the Dirac theory, formulated in a Minkowski spacetime with an arbitrary number of spatial dimensions. This is done by applying Hadamard's method of descent, which…
Applications of the Dirac equation with an anomalous magnetic moment are considered for description of characteristics of electrons, muons and quarks. The Dirac equation with four-dimensional scalar and vector potentials is reduced to a…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
A membrane technique, in which the symplectic and Ricci forms are integrated over surfaces in a complexification of the phase space, as well a ``creation" connection with zero curvature over lagrangian submanifolds, is used to obtain a…
In Foldy-Wouthuysen representation, we deduce the effective quantum mechanics for a particle confined to a curved surface by using the thin-layer quantization scheme. We find that the spin effect caused by confined potential as the results…
In this work it will be shown how quark confinement appears when wave equations derived in curved spaces are considered. First, the equations and their solutions for Coulomb-like potentials will be presented, and then, how this theory leads…
A relativistic equation is deduced for the bound state of two particles, by assuming a proper boundary condition for the propagation of the negative-energy states. It reduces to the (one-body)Dirac equation in the infinite limit of one of…
In this work we investigate the continuous confinement of quantum systems from three to two dimensions. Two different methods will be used and related. In the first one the confinement is achieved by putting the system under the effect of…
Various phenomena related to geometric phases in quantum mechanics are reviewed and explained by analyzing some examples.The concepts of 'parallelism' ,'connections' and 'curvatures' are applied to Aharonov-Bohm (AB) effect, to U(1)phase…
Using Weitzenb\"ock techniques on any compact Riemannian spin manifold we derive inequalities that involve a real parameter and join the eigenvalues of the Dirac operator with curvature terms. The discussion of these inequalities yields…
We determine what should correspond to the Dirac operator on certain quantized hermitian symmetric spaces and what its properties are. A new insight into the quantized wave operator is obtained.
On some specified convex supporting sets of spheres, we find a generalized longitude function whose level sets are totally geodesic. Given an arbitrary (weakly) harmonic map into spheres, the composition of the generalized longitude…
This paper introduces the modified version of Schwinger's quantization method, in which the information on constraints and the choice of gauge conditions are included implicitly in the choice of variations used in quantization scheme. A…
A new picture of Quantum Mechanics based on the theory of groupoids is presented. This picture provides the mathematical background for Schwinger's algebra of selective measurements and helps to understand its scope and eventual…
This manuscript provides a general approach to the investigation of field quantization in high-curvature geometries. The models and calculations can help with understanding the elastic and inelastic scattering of photons and electrons in…
This paper continues a geometric study of Harvey's Complex of Curves, whose ultimate goal is to apply the theory of hyperbolic spaces and groups to algorithmic questions for the Mapping Class Group and geometric properties of Kleinian…