The spin-statistics relation in nonrelativistic quantum mechanics and projective modules
Annales Mathématiques Blaise Pascal, Tome 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.

@article{AMBP_2004__11_2_205_0,
     author = {Papadopoulos, Nikolaos A. and Paschke, Mario and Reyes, Andr\'es and Scheck, Florian},
     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},
     volume = {11},
     number = {2},
     year = {2004},
     doi = {10.5802/ambp.193},
     mrnumber = {2109608},
     zbl = {1086.81056},
     language = {en},
     url = {www.numdam.org/item/AMBP_2004__11_2_205_0/}
}
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. http://www.numdam.org/item/AMBP_2004__11_2_205_0/

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