Related papers: Extending and quantising the Vogel plane
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…
This paper focuses on a new approach to plane geometry and develops important concepts that can allow researchers to unite and observe plane geometry from a new, meaningful perspective.
In near-field optics and optical tunneling theory, photon wave mechanics, i.e., the first quantized theory of the photon, allows us to address the spatial field localization problem in a flexible manner which links smoothly to classical…
On the base of symplectic quantum tomogram we define a probability distribution on the plane. The dual map transfers all observables which are polynomials of the position and momentum operators to the set of polynomials of two variables. In…
We study a system of two pointlike particles coupled to three dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two special-relativistic point particles in the centre of mass…
We explore the geometric notion of prolongations in the setting of computational algebra, extending results of Landsberg and Manivel which relate prolongations to equations for secant varieties. We also develop methods for computing…
Canonical quantization may be approached from several different starting points. The usual approaches involve promotion of c-numbers to q-numbers, or path integral constructs, each of which generally succeeds only in Cartesian coordinates.…
We propose a categorical and algebraic study of quantale modules. The results and constructions presented are also applied to abstract algebraic logic and to image processing tasks.
This work is a continuation of [1]. As in the previous article, here we will describe some interesting ideas and a lot of new theorems in plane geometry related to them.
Formal definitions of quantities, quantity spaces, dimensions and dimension groups are introduced. Based on these concepts, a theoretical framework and a practical algorithm for dimensional analysis are developed, and examples of…
A new space namely the Weyl-Kahler is proposed to the quantum state space. Some of the physical consequences are discussed.
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
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…
Quantization of $R^2$ and $S^1 \times S^1$ phase spaces are explicitly carried out tweaking the techniques of geometric quantization. Crucial is a combined use of left and right invariant vector fields. Canonical bases, operators and their…
An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…
An analogue of geometric quantization of Poisson algebras obtained by algebraic reduction of symmetries is developed. Interpretation of the obtained results and their application to the problem of commutativity of quantization and reduction…
Canonical quantization entails using Cartesian coordinates, and Cartesian coordinates exist only in flat spaces. This situation can either be questioned or accepted. In this paper we offer a brief and introductory overview of how a flat…
We consider an extension of Weyl geometry with the most general connection linearly determined by a vector field. We discuss some of the geometrical properties within this framework and then we construct gravitational theories leading to an…
Geometric quantization of a Poisson manifold need not imply quantization of its symplectic leaves. We provide the leafwise geometric quantization of a Poisson manifold, seen as a foliated one, whose quantum algebra restricted to each leaf…
The present thesis represents developments in two main directions related to the simple Lie algebras. The first one is devoted to the representation theory of the simple Lie algebras. Specifically, we present recent results, which include…