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The spin-statistics relation in nonrelativistic quantum mechanics and projective modules. (English) Zbl 1086.81056
Summary: In this work we consider non-relativistic quantum mechanics, obtained from a classical configuration space \({\mathcal Q}\) of indistinguishable particles. Following an approach proposed in M. Paschke Von Nichtkommutativen Geometrien, ihren Symmetrien und etwas Hochenergiephysik. Ph.D. thesis, Mainz University, 2001, wave functions are regarded as elements of suitable projective modules over \(C({\mathcal Q})\). We take furthermore into account the \(G\)-Theory point of view where the role of group action is particularly emphasized. As an example illustrating the method, the case of two particles is worked out in detail. Previous works [M. V. Berry and J. M. Robbins, Proc. R. Soc. Lond. A 453, 1771–1790 (1997; Zbl 0892.46084); J. Phys. A, Math. Gen., 33, L207–L2l4 (2001; Zbl 1010.81040)] aiming at a proof of a spin-statistics theorem for non-relativistic quantum mechanics are re-considered from the point of view of our approach, enabling us to clarify several points.

MSC:
81S05 Commutation relations and statistics as related to quantum mechanics (general)
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