Related papers: Canonical Group Quantization, Rotation Generators …
We examine mathematical questions around angle (or phase) operator associated with a number operator through a short list of basic requirements. We implement three methods of construction of quantum angle. The first one is based on operator…
In Dirac's canonical quantization theory on systems with second-class constraints, the commutators between the position, momentum and Hamiltonian form a set of algebraic relations that are fundamental in construction of both the quantum…
A quantum frame is defined by a material object subject to the laws of quantum mechanics. The present paper studies the relations between quantum frames, which in the classical case are described by elements of the Poincare' group. The…
We derive the effective angular momentum operator to $1/m^2$ and one-loop order in non-relativistic quantum electrodynamics (NRQED). In both dimensional and three-momentum-cutoff regularization schemes, we obtain the non-relativistic…
A revised program for generating the spin-angular coefficients in relativistic atomic structure calculations is presented. When compared with our previous version [G.Gaigalas, S.Fritzsche and I.P.Grant, CPC 139 (2001) 263], the new version…
Following the idea of a field quantization of gravity as realized in group field theory, we construct a minisuperspace model where the wavefunction of canonical quantum cosmology (either Wheeler-DeWitt or loop quantum cosmology) is promoted…
Born proposed a unification of special relativity and quantum mechanics that placed position, time, energy and momentum on equal footing through a reciprocity principle and extended the usual position-time and energy-momentum line elements…
We construct the quantum group $GL_q(2)$ as the semi-infinite cohomology of the tensor product of two braided vertex operator algebras based on the algebra $W_2$ with complementary central charges $c+\bar{c}=28$. The conformal field theory…
Quantum polyhedra constructed from angular momentum operators are the building blocks of space in its quantum description as advocated by Loop Quantum Gravity. Here we extend previous results on the semiclassical properties of quantum…
This article is a pedagogical introduction to relativistic quantum mechanics of the free Majorana particle. This relatively simple theory differs from the well-known quantum mechanics of the Dirac particle in several important aspects. We…
In quantum mechanics textbooks the momentum operator is defined in the Cartesian coordinates and rarely the form of the momentum operator in spherical polar coordinates is discussed. Consequently one always generalizes the Cartesian…
This paper presents the general theory of canonical transformations of coordinates in quantum mechanics. First, the theory is developed in the formalism of phase space quantum mechanics. It is shown that by transforming a star-product, when…
We discuss an extension of the quantization method based on the induced representation of the canonical group.
Using canonical quantisation, and eschewing the Schwinger-Keldysh path integral, we derive a version of the Worldline Quantum Field Theory (WQFT) formalism suitable for both scattering and bound configurations of the classical two-body…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
Canonical quantization (CQ) is built around $[Q,P]=i\hbar1\!\!1$, while affine quantization (AQ) is built around $[Q,D]=i\hbar\,Q$, where $D\equiv(PQ+QP)/2$. The basic CQ operators must fit $-\infty< P, Q <\infty$, while the basic AQ…
We develop a new mathematical approach to diffeomorphism invariant quantum states for the quantisation of general field theories such as general relativity and modified gravity. Treating quantum fields as fibre bundles, we discuss operators…
Let $\C$ be a sequence of multisets of subspaces of a vector space $\F_q^k$. We describe a practical algorithm which computes a canonical form and the stabilizer of $\C$ under the group action of the general semilinear group. It allows us…
We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…
A general scheme of construction and analysis of physical fields on the various homogeneous spaces of the Poincar\'{e} group is presented. Different parametrizations of the field functions and harmonic analysis on the homogeneous spaces are…