相关论文: Equivalence of Weyl Vacuum and Normal Ordered Vacu…
We study the features of the vacuum of the harmonic oscillator in the Moyal quantization. The vacuums with and without using the normal ordering look different. The vacuum without the normal ordering is shown to be expressed using the Weyl…
For the creation operator $\adag $ and the annihilation operator $a$ of a harmonic oscillator, we consider Weyl ordering expression of $(\adag a)^n$ and obtain a new symmetric expression of Weyl ordering w.r.t. $\adag a \equiv N$ and…
At high energy the standard model possesses conformal symmetry at the classical level. This is reflected at the quantum level by relations between the different beta functions of the model. These relations are known as the Weyl consistency…
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 generalize the Moyal equation, which describes the dynamics of quantum observables in phase space, to quantum systems coupled to a reservoir. It is shown that phase space observables become functionals of fluctuating noise forces…
We prove that Weyl quantization preserves constant of motion of the Harmonic Oscillator. We also prove that if $f$ is a classical constant of motion and $\mathfrak{Op}(f)$ is the corresponding operator, then $\mathfrak{Op}(f)$ maps the…
We examine a concrete realization of the quantum Weyl algebra and expand it to first order. From here we apply the resulting algebra to a quantum harmonic oscillator in its ground state and observe how a slightly noncommutative space…
In this investigation, the displacement operator is revisited. We established a connection between the Hermitian version of this operator with the well-known Weyl ordering. Besides, we characterized the quantum properties of a simple…
The Weyl quantization of classical observables on the torus (as phase space) without regularity assumptions is explicitly computed. The equivalence class of symbols yielding the same Weyl operator is characterized. The Heisenberg equation…
The star product and Moyal bracket are introduced using the coherent states corresponding to quantum systems with non-linear spectra. Two kinds of coherent state are considered. The first kind is the set of Gazeau-Klauder coherent states…
A normal form transformation is carried out on the operators of a complete set of commuting observables in a multidimensional, integrable quantum system, mapping them by unitary conjugation into functions of the harmonic oscillators in the…
Inspired by the fact that the Moyal quantization is related with nonlocal operation, I define a difference analogue of vector fields and rephrase quantum description on the phase space. Applying this prescription to the theory of the…
In this paper, we give a new approach for the study of Weyl-type theorems. Precisely we introduce the concepts of spectral valued and spectral partitioning functions. Using two natural order relations on the set of spectral valued…
An extension of the Weyl-Wigner-Moyal formulation of quantum mechanics suitable for a Dirac quantized constrained system is proposed. In this formulation, quantum observables are described by equivalent classes of Weyl symbols. The Weyl…
The Moyal quantization is described as a discretization of the classical phase space by using difference analogue of vector fields. Difference analogue of Lie brackets plays the role of Heisenberg commutators.
This work prolongs, using an operator method, the investigations started in our recent paper J. Math. Phys. 51., 102108 on the spectrum and states of the harmonic oscillator on twisted Moyal plane, where rather a Moyal-star-algebraic…
The Weyl-Wigner map yields the entire structure of Moyal quantum mechanics directly from the standard operator formulation. The covariant generalization of Moyal theory, also known as Vey quantum mechanics, was presented in the literature…
In this paper we study the quantum cosmology of homogeneous and isotropic cosmology, via the Weyl-Wigner-Groenewold-Moyal formalism of phase space quantization, with perfect fluid as a matter source. The corresponding quantum cosmology is…
A generalization of canonical quantization which maps a dynamical operator to a dynamical superoperator is suggested. Weyl quantization of dynamical operator, which cannot be represented as Poisson bracket with some function, is considered.…
We compute the Weyl symbol of the resolvent of the harmonic oscillator and study its properties.