Related papers: Canonical variables and analysis on so(n,2)
While dealing with a class of generalized Bargmann spaces, we rederive their reproducing kernels from the knowledge of an orthonormal basis by using an addition formula for Laguerre polynomials involving the disk polynomials. We construct…
We develop the quantum harmonic analysis framework in the reducible setting and apply our findings to polyanalytic Fock spaces. In particular, we explain some phenomena observed in arXiv:2201.10230 and answer a few related open questions.…
Affine coherent states are generated by affine kinematical variables much like canonical coherent states are generated by canonical kinematical variables. Although all classical and quantum formalisms normally entail canonical variables, it…
Phase operators are constructed using a Klauder-Berezin coherent state quantization in finite Hilbert subspaces of the Hilbert space of Fourier series. The study of infinite dimensional limits of mean values of some observables phase leads…
We present an original approach to quantization based on operator-valued measure that generalizes the so-called Berezin-Klauder-Toeplitz quantization, and more generally coherent state quantization approches.
We study regularization of matrices in the covariant derivative interpretation of matrix models, a typical example of which is the type IIB matrix model. The covariant derivative interpretation provides a possible way in which curved…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for…
Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part…
Canonical quantization of the photon -- a free massless vector field -- is considered in cosmological spacetimes in a two-parameter family of linear gauges that treat all the vector potential components on equal footing. The goal is setting…
In this paper, we construct coherent states for each generalized Bergman space on the n-dimensional complex projective space in order to apply a coherent states quantization method. Doing so allows to define the Berezin transform for these…
Interacting systems of particles with generalized statistics are considered on both classical and quantum level. It is shown that all possible quantum states and corresponding processes can be represented in terms of certain specific…
In the first half we make a short review of coherent states and generalized coherent ones based on Lie algebras su(2) and su(1,1), and the Schwinger's boson method to construct representations of the Lie algebras. In the second half we make…
We present a rigorous and functorial quantization scheme for affine field theories, i.e., field theories where local spaces of solutions are affine spaces. The target framework for the quantization is the general boundary formulation,…
We construct a modular generalized Springer correspondence for any classical group, by generalizing to the modular setting various results of Lusztig in the case of characteristic-$0$ coefficients. We determine the cuspidal pairs in all…
We construct equivariant quantization of a special family of Levi conjugacy classes of the complex orthogonal group $SO(N)$, whose stabilizer contains a Cartesian factor $SO(2)\times SO(P)$, $1\leqslant P<N$, $P\equiv N \mod 2$.
The affine coherent states quantization is a promising integral quantization of Hamiltonian systems when the phase space includes at least one conjugate pair of variables which takes values from a half-plane. Such a situation is common for…
Using the orthonormality of the 2D-Zernike polynomials, reproducing kernels, reproducing kernel Hilbert spaces, and ensuring coherent states attained. With the aid of the so-obtained coherent states, the complex unit disc is quantized.…
We study canonical models of $\left(\mathbb{Z}/k\mathbb{Z}\right)^n$- covers of the projective line, tamely ramified at exactly $n+1$ points each of index $k$, when $k,n\geq 2$ and the characteristic of the ground field $K$ is either zero…
The well-known theory of "rational canonical form of an operator" describes the invariant factors, or elementary divisors, as a complete set of invariants of a similarity class of an operator on a finite-dimensional vector space $\V$ over a…
A general scheme is proposed for constructing vector coherent states, in analogy with the well-known canonical coherent states, and their deformed versions, when these latter are expressed as infinite series in powers of a complex variable…