Dirac Oscillator in Noncommutative Phase Space

We study the Dirac oscillators in a noncommutative phase space. The results show that the energy gap of Dirac oscillator was changed by noncommutative effect. In addition, we obtain the non-relativistic limit of the energy spectrum.     

非对易相空间中角动量的分裂

非对易空间效应是一种在弦尺度下出现的物理效应. 本文首先介绍了在Schwinger表象中角动量的3个分量用产生--消灭算符的表示形式, 接着讨论了非对易相空间的量子力学代数; 然后用对易空间谐振子的产生-消灭算符表示出了在非对易情况下的角动量; 最后讨论了非对易相空间中角动量的分裂.     

Hydrogen Atom Spectrum in Noncommutative Phase Space

We study the energy levels of the hydrogen atom in the noncommutative phase space with simultaneous spacespace and momentum-momentum noncommutative relations, We find new terms compared to the case that only noncommutative space-space relations are assumed. We also present some comments on a previous paper [Alavi S A hep-th/0501215].     

Relativistic Hydrogen-Like Atom on a Noncommutative Phase Space

The energy levels of hydrogen-like atom on a noncommutative phase space were studied in the framework of relativistic quantum mechanics. The leading order corrections to energy levels 2S _1/2, 2P _1/2 and 2P _3/2 were obtained by using the ?? and the \(\bar \theta \) modified Dirac Hamiltonian of hydrogen-like atom on a noncommutative phase space. The degeneracy of the energy levels 2P _1/2 and 2P _3/2 were removed completely by ??-correction. And the \(\bar \theta \)-correction shifts these energy levels.     

On Quantum Mechanics on Noncommutative Quantum Phase Space

In this work, we develop a general framework in which Noncommutative Quantum Mechanics (NCQM), characterized by a space noncommutativity matrix parameter θ=ε_ij^k θ_k and a momentum noncommutativity matrix parameter β=ε_ij^k β_k, is shown to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS). Imposing some constraints on this particular transformation, we firstly find that the product of the two parameters θ and β possesses a lower bound in direct relation with Heisenberg incertitude relations, and secondly that the two parameters are equivalent but with opposite sign, up to a dimension factor depending on the physical system under study. This means that noncommutativity is represented by a unique parameter which may play the role of a fundamental constant characterizing the whole NCQPS. Within our framework, we treat some physical systems on NCQPS : free particle, harmonic oscillator, system of two-charged particles, Hydrogen atom. Among the obtained results, we discover a new phenomenon which consists of a free particle on NCQPS viewed as equivalent to a harmonic oscillator with Larmor frequency depending on β, representing the same particle in presence of a magnetic field $\vec{B}=q^{-1}\vec{\beta}$. For the other examples, additional correction terms depending on β appear in the expression of the energy spectrum. Finally, in the two-particle system case, we emphasize the fact that for two opposite charges noncommutativity is effectively feeled with opposite sign.     

非对易相空间中各向同性谐振子的能级分裂

非对易空间的效应是出现在弦尺度下的一种物理效应. 本文介绍了量子力学非对易空间的代数关系; 讨论了非对易相空间中服从玻色-爱因斯坦统计的粒子的连续性条件, 最后给出了非对易相平面和非对易相空间中的线性谐振子的能级分裂.     

Wigner Functions for the Bateman System on Noncommutative Phase Space

We study an important dissipation system, i.e. the Bateman model on noncommutative phase space. Using the method of deformation quantization, we calculate the Exp functions, and then derive the Wigner functions and the corresponding energy spectra.     

DKP Oscillator with Spin-0 in Three-dimensional Noncommutative Phase Space

The DKP equation with Dirac oscillator potential for spin-0 particles has been studied when both space-space noncommutativity and momentum-momentum noncommutativity are considered. The exact wave functions and corresponding energy levels have been found. Due to the noncommutative effect, the energy spectrum is not degenerate.     

电磁场中带电粒子在非对易相空间的能级

非对易空间效应是出现在弦的尺度下的一种物理效应。 首先扼要介绍了非对易相空间中的量子力学代数、 Moyal Weyl乘法和广义Bopp变换, 然后讨论了电磁场中带电粒子的Hamiltonian算符, 最后给出了其在非对易相空间中的能级情况。     

Klein-Gordon Oscillator in Noncommutative Phase Space Under a Uniform Magnetic Field

Using a direct substitution method, Klein-Gordon oscillator in a uniform magnetic field is researched in the noncommutative phase space (NCPS), the corresponding exact energy is obtained, and the analytic eigenfunction is presented in terms of the confluent hypergeometric. It is shown that the Klein-Gordon oscillator in uniform magnetic field in noncommutative phase space has the similar behaviors to the Landau problem in commutative space. In addition, the non-relativistic limit of the energy spectrum is obtained.     

Deformations of Fluid Dynamics and Friedmann Equation on Noncommutative Phase Space

Noncommutative phase space is one of the widely studied extensions of ordinary phase space, and has profound implications in cosmological physics. In this paper we study the dynamics of perfect fluid on noncommutative phase space, as well as deformations of the Friedmann equation. The Lagrangian formalism is used to take into account of the phase space noncommutativities. Then a map from canonical Lagrangian variables to Eulerian variables is employed to derive the equations of motion of the mass and current densities. We find that both these two equations receive noncommutative corrections that are linear in the noncommutative parameters. However, we also find that in the approximation of vanishing comoving velocity the leading order noncommutative correction due to momentum noncommutativity on the Friedmann equation is zero.     

Dirac Oscillator in Noncommutative Phase Space and (Anti)-Jaynes-Cummings Models

We study planar Dirac oscillator in noncommutative phase space. The model is solved exactly. The relation between this model and Jaynes-Cummings (JC) or anti-Jaynes-Cummings (AJC) models is investigated. We find that the behaviors of this model depend qualitatively on the signs of a dimensionless parameter κ. For a negative κ, we find that there is a map from this model to a model which contains only AJC terms. However, for a positive κ, there is a map from this model to a model which contains both AJC and JC terms simultaneously. Our investigation may afford a new way to study the noncommutative Dirac oscillator by means of quantum optics method, and vice verse.     

The Harmonic Oscillator Influenced by Gravitational Wave in Noncommutative Quantum Phase Space

Dynamical property of harmonic oscillator affected by linearized gravitational wave (LGW) is studied in a particular case of both position and momentum operators which are noncommutative to each other. By using the generalized Bopp’s shift, we, at first, derived the Hamiltonian in the noncommutative phase space (NPS) and, then, calculated the time evolution of coordinate and momentum operators in the Heisenberg representation. Tiny vibration of flat Minkowski space and effect of NPS let the Hamiltonian of harmonic oscillator, moving in the plain, get new extra terms from it’s original and noncommutative space partner. At the end, for simplicity, we take the general form of the LGW into gravitational plain wave, obtain the explicit expression of coordinate and momentum operators.     

He-McKellar-Wilkens Effect in Noncommutative Space

The He-McKellar-Wilkens （HMW） effect in non-commutative （NC） space is studied. By solving the Dirac equations on NC space, we obtain topological HMW phase in NC space where the additional terms related to the space non-commutativity are given explicitly.     

On the Generalized Phase Space Approach to Duffin-Kemmer-Petiau Particles

We present a general derivation of the Duffin-Kemmer-Petiau (D.K.P) equation on the relativistic phase space proposed by Bohm and Hiley. We consider geometric algebras and the idea of algebraic spinors due to Riesz and Cartan. The generators ^(p) of the D.K.P algebras are constructed in the standard fashion used to construct Clifford algebras out of bilinear forms. Free D.K.P particles and D.K.P particles in a prescribed external electromagnetic field are analized and general Liouville type equations for these cases are obtained. Choosing particular values for the label p we classify the different types of the D.K.P Liouville operators.     

DKP Oscillator in a Noncommutative Space

We present the DKP oscillator model of spins 0 and 1, in a noncommutative space. In the case of spin 0, the equation is reduced to Klein Gordon oscillator type, the wave functions are then deduced and compared with the DKP spinless particle subjected to the interaction of a constant magnetic field. For the case of spin 1, the problem is equivalent with the behavior of the DKP equation of spin 1 in a commutative space describing the movement of a vectorial boson subjected to the action of a constant magnetic field with additional correction which depends on the noncommutativity parameter.     

DKP Oscillator in a Noncommutative Space

We present the DKP oscillator model of spins 0 and 1, in a noncommutative space. In the case of spin 0, the equation is reduced to Klein-Gordon oscillator type, the wave functions are then deduced and compared with the DKP spinless particle subjected to the interaction of a constant magnetic field. For the case of spin 1, the problem is equivalent with the behavior of the DKP equation of spin 1 in a commutative space describing the movement of a vectorial boson subjected to the action of a constant magnetic field with additional correction which depends on the noncommutativity parameter.     

Noncommutative Brownian Motion in Monotone Fock Space

An example of noncommutative Brownian motion is constructed on the monotone Fock space which is a kind of “Fock space” generated by all the decreasing finite sequences of positive real numbers. The probability distribution at time associated to this Brownian motion is shown to be the arcsine law normalized to mean 0 and variance t. Received: 15 March 1996\,/\,Accepted: 2 July 1996     

Feynman Rules and Generalized Ward Identities in Phase Space Functional Integral

Based on the phase-space generating functional of Green function, the generalizedcanonical Ward identities are derived It is point out that one can deduce Feynmanrules in tree approximation without carring out explicit integration over canonicalmomenta in phase-space generating functional. If one adds a four-dimensionaldivergence term to a Lagrangian of the field, then, the propagator of the field can bechanged.