ABSTRACT In this article I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non-Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement with many physicists, ensures that Galilei invariance is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally, I show how this favours a nomological rather than an ontological view of the wave function.

中文翻译：

---

波动函数的名词解释的新论点：伽利略群和非相对论量子力学的经典极限

摘要在本文中，我将在非相对论量子力学中对波函数的现实解释的框架内，研究波函数的数学和物理性质。我反对这样一种观点，即在数学上，波动函数是配置空间上的两分量标量场。首先，我回顾一下这种观点如何使量子力学成为非伽利略不变的，并得出错误的经典极限。此外，我认为与许多物理学家一样，将波函数解释为射线可以确保伽利略不变性得到保留。此外，我将讨论波函数与规范势而不是场的行为如何相似。最后，我展示了这是如何支持波动函数的法理学而非本体论的观点。