Related papers: Coherent State Transforms and the Weyl Equation in…
We study the canonical quantization of the induced 2d-gravity and the pure gravity CGHS-model on a closed spatial section. The Wheeler-DeWitt equations are solved in (spatially homogeneous) choices of the internal time variable and the…
In this paper we define a causal Lorentz covariant noncommutative (NC) classical Electrodynamics. We obtain an explicit realization of the NC theory by solving perturbatively the Seiberg-Witten map. The action is polynomial in the field…
Particular boundary correlation functions of conformal field theory are needed to answer some questions related to random conformally invariant curves known as Schramm-Loewner evolutions (SLE). In this article, we introduce a correspondence…
The Weyl algebra,- the usual C*-algebra employed to model the canonical commutation relations (CCRs), has a well-known defect in that it has a large number of representations which are not regular and these cannot model physical fields.…
For arbitrary quantizable compact Kaehler manifolds, relations between the geometry given by the coherent states based on the manifold and the algebraic (projective) geometry realised via the coherent state mapping into projective space,…
We describe an explicit connection between solutions to equations $Df=0$ (the Generalized Cauchy-Riemann equation) and $(D+M)f=0$, where operators $D$ and $M$ commute. The described connection allows to construct a ``function theory'' (the…
We present a covariant quantum formalism for scalar particles based on an enlarged Hilbert space. The particular physical theory can be introduced through a timeless Wheeler DeWitt-like equation, whose projection onto four-dimensional…
We study solutions of the Bogomolny equation on R^2\times S^1$ with prescribed singularities. We show that Nahm transform establishes a one-to-one correspondence between such solutions and solutions of the Hitchin equations on a punctured…
We construct the coherent states in the sense of Gilmore and Perelomov for the fermionic Fock space. Our treatment is from the outset adapted to the infinite-dimensional case. The fermionic Fock space becomes in this way a reproducing…
We extend a quantized skew Howe duality result for Type $\mathbf{A}$ algebras to orthogonal types via a seesaw. We develop an operator commutant version of the First Fundamental Theorem of invariant theory for $U_q(\mathfrak{so}_n)$ using a…
This work describes coherent states for a physical system governed by a Hamiltonian operator, in two dimensional space, of spinless charged particles subject to a perpendicular magnetic field B, coupled with a harmonic potential. The…
We study the ergodic properties of eigenfunctions of Schr\"odinger operators on a closed connected Riemannian manifold $M$ in case that the underlying Hamiltonian system possesses certain symmetries. More precisely, let $M$ carry an…
A gauge theory of solids with conformal symmetry is formulated to model various electromechanical and magnetomechanical coupling phenomena. If the pulled back metric of the current configuration (the right Cauchy-Green tensor) is scaled…
The presentation makes use of geometric algebra, also known as Clifford algebra, in 5-dimensional spacetime. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from…
I show how the isomorphism between the Lie groups of types $B_2$ and $C_2$ leads to a faithful action of the Clifford algebra $\mathcal C\ell(3,2)$ on the phase space of 2-dimensional dynamics, and hence to a mapping from Dirac spinors…
The Hilbert space effect algebra is a fundamental mathematical structure which is used to describe unsharp quantum measurements in Ludwig's formulation of quantum mechanics. Each effect represents a quantum (fuzzy) event. The relation of…
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…
The traditional Chern-Simons (CS) terms in 3+1 dimensions that modify General Relativity (GR), Quantum Chromodynamics (QCD), and Quantum Electrodynamics (QED), typically lack scale invariance. However, a locally scale invariant and…
In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product $|z\rangle \langle z|$. Because no pair of coherent states is orthogonal, one…
The Schur-Weyl states belong to a special class of states with a symmetry described by two Young and Weyl tableaux. Representation of physical systems in Hilbert space spanned on these states enables to extract quantum information hidden in…