Related papers: Extending and quantising the Vogel plane
A formulation of Covariant Canonical Quantization is discussed, which works on an extended Hilbert space and reduces to conventional canonical quantization when constraining to the solution of the field equation a priori. From the formal…
In this paper we will give two different natural generalizations of compact spaces and connected spaces simultaneously. We will show that these generalizations coincide for the subspaces of the real line and that they differ for subspaces…
In a previous paper we have introduced a class of multiplications of distributions in one dimension. Here we furnish different generalizations of the original definition and we discuss some applications of these procedures to the…
Let g be a Lie bialgebra and let V be a finite-dimensional g-module. We study deformations of the symmetric algebra of V which are equivariant with respect to an action of the quantized enveloping algebra of g. In particular we investigate…
An introductory overview of vector spaces, algebras, and linear geometries over an arbitrary commutative field is given. Quotient spaces are emphasized and used in constructing the exterior and the symmetric algebras of a vector space.…
We apply the topological quantization method to some gravitational fields which can be represented as generalized harmonic maps. This representation extends the well-known concept of harmonic maps and allows us to describe some solutions to…
The paper presents shortly the geometric approach to the problem of a general quantization formalism, both physically meaningful and mathematically consistent.
The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…
Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…
In this paper we study the problem of quantizing theories defined over a nonclassical configuration space. If one follows the path-integral approach, the first problem one is faced with is the one of definition of the integral over such…
We study the generalized analogues of conics for normed planes by using the following natural approach: It is well known that there are different metrical definitions of conics in the Euclidean plane. We investigate how these definitions…
We compute the cohomology of the right generalised projective Stiefel manifolds and use it to find bounds on the rank of the complementary bundle for certain vector bundles. Further the cohomology computations are also used to find bounds…
We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hindsight there are many examples of graded bundles that appear…
Suggestions concerning the generalization of the geometric quantization to the case of nonlinear field theories are given. Results for the Liouville field theory are presented.
This paper is a survey of author's mathematical and logical study of the problem of quantization of fields.
Finite dimensional representations of extended Weyl-Heisenberg algebra are studied both from mathematical and applied viewpoints. They are used to define unitary phase operator and the corresponding eigenstates (phase states). It is also…
We introduce a new geometric constant based on a generalization of the parallelogram law, and study its properties as well as some relationships with other well-known geometric constants. A sufficient condition for normal structure is…
We construct a mathematical version of quantum field theory. It assigns to a multidimensional variational principle an associative algebra which is a quantization of the Poisson algebra of classical field theory observables. For free scalar…
The classical time of arrival in the interacting case is quantized by way of quantizing its expansion about the free time of arrival. The quantization is formulated in coordinate representation which represents ordering rules in terms of…
The prerequisites of the extended phase space approach to quantization of gravity, which is alternative to the Wheeler-DeWitt one and other existing approaches, are presented. The features of the proposed approach and conclusions from its…