A set of gauge transformations of a relativistic field of quantum harmonic oscillators is studied in a mathematically rigorous manner. Each wave function in the domain of the number operator of a single oscillator generates a Fréchet-differentiable field of wave functions. Starting from a coherent wave function one obtains a two-dimensional differentiable manifold of coherent vector states. As an illustration it is shown that the gauge transformation can be chosen in such a way that the resulting fields describe a freely-propagating wave.

中文翻译：

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量子谐振子相对论场的量规变换

以数学上严格的方式研究了一组量子谐波振荡器相对论场的规范变换。单个振荡器的数字运算符域中的每个波动函数都会产生波动函数的Fréchet可微分场。从相干波函数开始，可以获得相干矢量状态的二维微分流形。如图所示，可以选择量规变换，使得所得场描述自由传播的波。