In this work we consider non-relativistic quantum mechanics, obtained from a classical configuration space of indistinguishable particles. Following an approach proposed in [8], wave functions are regarded as elements of suitable projective modules over . We take furthermore into account the -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}, zbl = {1086.81056}, mrnumber = {2109608}, language = {en}, url = {http://www.numdam.org/articles/10.5802/ambp.193/} }
TY - JOUR AU - Papadopoulos, Nikolaos A. AU - Paschke, Mario AU - Reyes, Andrés AU - Scheck, Florian TI - The spin-statistics relation in nonrelativistic quantum mechanics and projective modules JO - Annales mathématiques Blaise Pascal PY - 2004 SP - 205 EP - 220 VL - 11 IS - 2 PB - Annales mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.193/ DO - 10.5802/ambp.193 LA - en ID - AMBP_2004__11_2_205_0 ER -
%0 Journal Article %A Papadopoulos, Nikolaos A. %A Paschke, Mario %A Reyes, Andrés %A Scheck, Florian %T The spin-statistics relation in nonrelativistic quantum mechanics and projective modules %J Annales mathématiques Blaise Pascal %D 2004 %P 205-220 %V 11 %N 2 %I Annales mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.193/ %R 10.5802/ambp.193 %G en %F 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, Volume 11 (2004) no. 2, pp. 205-220. doi : 10.5802/ambp.193. http://www.numdam.org/articles/10.5802/ambp.193/
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