Possibility of obtaining a non-relativistic proof of the spin-statistics theorem in the Galilean frame

Details Possibility of obtaining a non-relativistic proof of the spin-statistics theorem in the Galilean frame Possibility of obtaining a non-relativistic proof of the spin-statistics theorem in the Galilean frame

2004-07-27

arxiv.org/abs/quant-ph/0407208v3

Physics

Quantum Physics

7 pages, 1 Postscript figure; v2: added a new section, enlarged introduction and conclusion; v3: added new comments and correc

Scientific paper

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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