Related papers: Canonical quantization of motion on submanifolds

This work constitutes the second part of a series of studies that aim to utilise tools from Hamiltonian mechanics to investigate the motion of an extended body in general relativity. The first part of this work [Refs. [1, 2]] constructed a…

The electromagnetic field is canonically quantized in the presence of a linear, dispersive and dissipative medium that is in uniform motion. Specifically we calculate the change in the normal modes of the coupled matter-field system and…

In this work, Schr\"odinger and Dirac equations will be examined in geometries that confine the particles to hypersurfaces. For this purpose, two methods will be considered. The first method is the thin layer method which relies on explicit…

This work is a continuation of our previous works concerning linear canonical transformations and phase space representation of quantum theory. It is mainly focused on the description of an approach which allows to establish spinorial…

Starting with the first-order singular Lagrangian, the problem of the quantization of a dynamical system constrained to a submanifold embedded in the higher-dimensional Euclidean space is investigated within the framework of operatorial…

The results, different aspects and applications of our method of quantisation on configuration manifolds - called Borel Quantisation - were presented at meetings of the series `Symmetries in Science' and can be found in the published…

This article continues and completes our previous work [14] J. Phys. Commun. 2 (2018) 025007. First of all, we present two methods of quantization associated with a linear connection given on a differentiable manifold, one of them being the…

The diffculties of relativistic particle theories formulated my means of canonical quantization, such as Klein-Gordon and Dirac theories, ultimately led theoretical physicists to turn on quantum field theory to model elementary particle…

We consider the motion of a quantum particle whose position is measured in random places at random moments in time. We show that a freely moving particle measured in this way undergoes superdiffusion, while a charged particle moving in a…

Canonical quantization of electromagnetic field is traditionally done using plane waves. It is possible to formulate the quantization using other complete set of basis functions. Wavelets are a special kind of functions which are localized…

We present quantization of particle dynamics on one-sheet hyperboloid embedded in three dimensional Minkowski space. Taking account of all global symmetries enables unique quantization. Making use of topology of canonical variables not only…

New, gauge-independent, second-order Lagrangian for the motion of classical, charged test particles is used to derive the corresponding Hamiltonian formulation. For this purpose a Hamiltonian description of the theories derived from the…

Quantization of the free Maxwell field in Minkowski space is carried out using a loop representation and shown to be equivalent to the standard Fock quantization. Because it is based on coherent state methods, this framework may be useful…

We have discovered a class of dynamically stable coherent states for motion on the half-line. The regularization of the half-line boundary and the consequent quantum motion are expounded within the framework of covariant affine…

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…

This book is an attempt to build a consistent relativistic quantum theory of interacting particles. In the first part of the book "Quantum electrodynamics" we follow rather traditional approach to particle physics. Our discussion proceeds…

A generalized canonical form of multi-time dynamical theories is proposed. This form is a starting point for a modified canonical quantization procedure of theories based on a quantum version of the action principle. As an example, the…

I study the canonical formulation and quantization of some simple parametrized systems, including the non-relativistic parametrized particle and the relativistic parametrized particle. Using Dirac's formalism I construct for each case the…

With the purpose to introduce a useful tool for researches concerning foundations of quantum mechanics and applications to quantum technologies, here we study three quantumness quantifiers for bipartite optical systems: one based on…

Second quantization of a classical nonrelativistic one-particle system as a deformation quantization of the Schrodinger spinless field is considered. Under the assumption that the phase space of the Schrodinger field is $C^{\infty}$, both,…