论文标题
半线的仿射量化
Affine Quantization on the Half Line
论文作者
论文摘要
经典物理和量子物理学之间的相似性足够大，可以对量化方法进行研究。正如历史所表明的那样，在$ \ mathbb {r}^n $的常规量子力学的情况下，狄拉克的规范量化方法效果很好，但在非平凡的相位空间中可能会失败，并且也因订购问题而受苦。仿射量化是一种类似于规范量化的替代方法，在规范量化失败的情况下可能会带来积极的结果。在本文中，我们在半线上重新审视了仿射量化方法。我们制定并解决了一些简单的模型，即自由粒子和谐波振荡器。
The similarity between classical and quantum physics is large enough to make an investigation of quantization methods a worthwhile endeavour. As history has shown, Dirac's canonical quantization method works reasonably well in the case of conventional quantum mechanics over $\mathbb{R}^n$ but it may fail in non-trivial phase spaces and also suffer from ordering problems. Affine quantization is an alternative method, similar to the canonical quantization, that may offer a positive result in situations for which canonical quantization fails. In this paper we revisit the affine quantization method on the half line. We formulate and solve some simple models, the free particle and the harmonic oscillator.
