论文标题
HOPF捆绑中QED的非扰动量化方法
Nonperturbative quantization approach for QED on the Hopf bundle
论文作者
论文摘要
我们考虑dirac方程和麦克斯韦的电动力学，$ \ mathbb {r} \ times s^3 $ spacetime，其中三维球是hopf bundle $ s^3 \ rightarrow s^2 $。在这两种情况下，都获得了经典溶液的离散光谱。基于获得的解决方案，进行了自由，非互动狄拉克和麦克斯韦场的量化。提出了相互作用的狄拉克和麦克斯韦场的非扰动量化方法。写下了相应的操作员方程和Green功能的Schwinger-Dyson方程的无限集。为了说明建议的非扰动量化方案，我们编写了一组简化的方程式，描述了某些物理情况。此外，我们讨论了量子状态的属性和相互作用场的运算符。
We consider the Dirac equation and Maxwell's electrodynamics in $\mathbb{R} \times S^3$ spacetime, where a three-dimensional sphere is the Hopf bundle $S^3 \rightarrow S^2$. In both cases, discrete spectra of classical solutions are obtained. Based on the solutions obtained, the quantization of free, noninteracting Dirac and Maxwell fields is carried out. The method of nonperturbative quantization of interacting Dirac and Maxwell fields is suggested. The corresponding operator equations and the infinite set of the Schwinger-Dyson equations for Green's functions is written down. To illustrate the suggested scheme of nonperturbative quantization, we write a simplified set of equations describing some physical situation. Also, we discuss the properties of quantum states and operators of interacting fields.
