伽利略坐标系下自旋统计定理非相对论性证明的可能性
Possibility of obtaining a non-relativistic proof of the spin-statistics theorem in the Galilean frame
摘要：
在这里，我们探讨了获得自旋统计定理的非相对论性证明的可能性。首先，我们研究了结构的公理和定理中涉及的相对论性施温格样证明的自旋统计关系。其次，从这个结构出发，我们确定相对论假设。最后，我们重新制定这些假设，以获得伽利略证明。我们的结论是，自旋统计定理不能推导到三维空间的伽利略量子场论的框架，因为需要证明定理的两个假设是不相容的。然而，我们分析的条件下，一个非相对主义的证明仍然可以推导出来。
英文摘要：
Here we explore the possibility to obtain a non-relativistic proof of the spin-statistics theorem. First, we examine the structure of axioms and theorems involved in a relativistic Schwinger-like proof of the spin-statistics relation. Second, starting from this structure we identify the relativistic assumptions. Last, we reformulate these assumptions in order to obtain a Galilean proof. We conclude that the spin-statistics theorem cannot be deduced into the framework of Galilean quantum field theories for three space dimensions because two of the assumptions needed to prove the theorem are incompatible. We analyze, however, the conditions under which a non-relativist proof could still be deduced.
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