The spin-statistics relation in nonrelativistic quantum mechanics and projective modules
Annales mathématiques Blaise Pascal, Volume 11 (2004) no. 2, pp. 205-220.

In this work we consider non-relativistic quantum mechanics, obtained from a classical configuration space 𝒬 of indistinguishable particles. Following an approach proposed in [8], wave functions are regarded as elements of suitable projective modules over C(𝒬). We take furthermore into account the G-Theory point of view (cf. [HPRS,S]) 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 (cf. [BR1,BR2]) 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.

DOI: 10.5802/ambp.193
Nikolaos A. Papadopoulos 1; Mario Paschke 2; Andrés Reyes 1; Florian Scheck 1

1 Johannes-Gutenberg-Universität Institut für Physik - ThEP. Staudinger Weg 7 Mainz, D-55128 Germany
2 Max Planck Institute for Mathematics in the Sciences Inselstrasse 22-26 Leipzig, D-04103 Germany
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Nikolaos A. Papadopoulos; Mario Paschke; Andrés Reyes; Florian Scheck. The spin-statistics relation in nonrelativistic quantum mechanics and projective modules. Annales mathématiques Blaise Pascal, Volume 11 (2004) no. 2, pp. 205-220. doi : 10.5802/ambp.193. https://ambp.centre-mersenne.org/articles/10.5802/ambp.193/

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