论文标题
扩展Snyder模型的量子力学
Quantum mechanics of the extended Snyder model
论文作者
论文摘要
我们根据扩展的Snyder模型研究了量子机械谐波振荡器。 Snyder模型的这种实现是由$ d $空间坐标产生的量子相空间，以及$ d（d-1）/2 $张力的自由度，以及他们的共轭动量。 \ coo遵守非欺骗\ cor并生成非交通性几何形状，该几何形状与模型的通常实现相比，它的性质更高，特别是引起了关联的星星。 通过引入创建和歼灭操作员研究谐波振荡器的光谱。讨论了引入其他自由度的一些物理后果。
We investigate a quantum mechanical harmonic oscillator based on the extended Snyder model. This realization of the Snyder model is constructed as a quantum phase space generated by $D$ spatial coordinates and $D(D-1)/2$ tensorial degrees of freedom, together with their conjugate momenta. The \coo obey nontrivial \cor and generate a noncommutative geometry, which admits nicer properties than the usual realization of the model, in particular giving rise to an associative star product. The spectrum of the harmonic oscillator is studied through the introduction of creation and annihilation operators. Some physical consequences of the introduction of the additional degrees of freedom are discussed.
