Related papers: On the Invertibility of Born-Jordan Quantization
A quantization over a manifold can be seen as a way to construct a differential operator with prescribed principal symbol. The quantization map is moreover required to be a linear bijection. It is known that there is in general no natural…
We start from the quantum Miura transformation [7] for the $W$-algebra associated with $GL(n)$ group and find an evident formula for quantum L-operator as well as for the action of $W_l$ currents (l=1,..,n) on elements of the completely…
In this work, we present straightforward and concrete computations of the unitary irreducible representations of the Euclidean motion group $M(2)$ employing the methods of deformation quantization. Deformation quantization is a quantization…
We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inflation. It has recently been argued that when identical copies of a quantum measurement system exist,…
Suppose $\lambda_1$ and $\lambda_2$ are infinitely divisible Radon measures on real Banach spaces $E_1$ and $E_2$, respectively and let $T:E_{1} \rightarrow E_{2}$ be a Borel measurable mapping so that $T(\lambda_1) * \rho = \lambda_2 $ for…
Exact solution to many problems in mathematical physics and quantum field theory often can be expressed in terms of an algebraic curve equipped with a meromorphic differential. Typically, the geometry of the curve can be seen most clearly…
This is a noncommutative version of the previous work entitled "Deformation Expression for Elements of Algebras (I)." In general in a noncommutative algebra, there is no canonical way to express elements in univalent way, which is often…
In this paper, the linear differential expression of order $n \ge 2$ with distribution coefficients of various singularity orders is considered. We obtain the associated matrix for the regularization of this expression. Furthermore, we…
The theme of this work is that the theory of charged particles in a uniform magnetic field can be generalized to a large class of operators if one uses an extended a class of Weyl operators which we call "Landau--Weyl pseudodifferential…
We analyze the polymer representation of quantum mechanics within the deformation quantization formalism. In particular, we construct the Wigner function and the star-product for the polymer representation as a distributional limit of the…
The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are obtained by means of bijective maps of the operators acting in…
We study non-elliptic quadratic differential operators. Quadratic differential operators are non-selfadjoint operators defined in the Weyl quantization by complex-valued quadratic symbols. When the real part of their Weyl symbols is a…
We study the Moyal quantization for the constrained system. One of the purposes is to give a proper definition of the Wigner-Weyl(WW) correspondence, which connects the Weyl symbols with the corresponding quantum operators. A Hamiltonian in…
We develop Weyl-Titchmarsh theory for Schroedinger operators with strongly singular potentials such as perturbed spherical Schroedinger operators (also known as Bessel operators). It is known that in such situations one can still define a…
We investigate the Weyl-Wigner-Gr\"oenewold-Moyal, the Stratonovich and the Berezin group quantization schemes for the space-space noncommutative Heisenberg-Weyl group. We show that the $\star$-product for the deformed algebra of Weyl…
Second quantization of a classical nonrelativistic one-particle system as a deformation quantization of the Schrodinger spinless field is considered. Under the assumption that the phase space of the Schrodinger field is $C^{\infty}$, both,…
A seminal theorem due to Weyl states that if (a_n) is any sequence of distinct integers, then, for almost every real number x, the sequence (a_n x) is uniformly distributed modulo one. In particular, for almost every x in the unit interval,…
We develop a quantization method, that we name decomposable Weyl quantization, which ensures that the constants of motion of a prescribed finite set of Hamiltonians are preserved by the quantization. Our method is based on a structural…
We study a class of quadratic time-frequency representations that, roughly speaking, are obtained by linear perturbations of the Wigner transform. They satisfy Moyal's formula by default and share many other properties with the Wigner…
Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum…