用Schwinger方法研究非相对论性耦合子
Non-Relativistic Propagators via Schwinger's Method
摘要：
为了推广所谓的Schwinger方法，我们重新考虑了两个非相对论系统的Feynman传播子：均匀磁场中的带电粒子和均匀磁场中的带电谐振子。我们不求解位置和正则动量算符${\bf R}$和${\bf P}$的海森堡方程，而是通过求解规范不变算符${\bf R}$和$\mathversion{bold}$ π $ = {\bf P}-e{\bf A}$的海森堡方程来应用这种方法，后者是力学动量算符。在我们的过程中，我们避免固定的规范从一开始，从而获得的结果表明明确的规范依赖的费曼传播子。
英文摘要：
In order to popularize the so called Schwinger's method we reconsider the Feynman propagator of two non-relativistic systems: a charged particle in a uniform magnetic field and a charged harmonic oscillator in a uniform magnetic field. Instead of solving the Heisenberg equations for the position and the canonical momentum operators, ${\bf R}$ and ${\bf P}$, we apply this method by solving the Heisenberg equations for the gauge invariant operators ${\bf R}$ and $\mathversion{bold}$π$ = {\bf P}-e{\bf A}$, the latter being the mechanical momentum operator. In our procedure we avoid fixing the gauge from the beginning and the result thus obtained shows explicitly the gauge dependence of the Feynman propagator.
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