Geodesic
The spin-statistics relation in nonrelativistic quantum mechanics and projective modules
Papadopoulos, Nikolaos A.1 ; Paschke, Mario2 ; Reyes, Andrés1 ; Scheck, Florian1
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
Annales mathématiques Blaise Pascal, Tome 11 (2004) no. 2, pp. 205-220

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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

Papadopoulos, Nikolaos A. 1 ; Paschke, Mario 2 ; Reyes, Andrés 1 ; Scheck, Florian 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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     title = {The spin-statistics relation in nonrelativistic quantum mechanics and projective modules},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {205--220},
     publisher = {Annales math\'ematiques Blaise Pascal},
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Papadopoulos, Nikolaos A.; Paschke, Mario; Reyes, Andrés; Scheck, Florian. The spin-statistics relation in nonrelativistic quantum mechanics and projective modules. Annales mathématiques Blaise Pascal, Tome 11 (2004) no. 2, pp. 205-220. doi: 10.5802/ambp.193

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