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 $C\left(𝒬\right)$. 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.

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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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[2] M.V. Berry; J.M. Robbins Indistinguishability for quantum particles: spin, statistics and the geometric phase, Proc. R. Soc. Lond. A, Volume 453 (1997), pp. 1771-1790 | Article | MR: 1469170 | Zbl: 0892.46084

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[4] A. Heil; N.A. Papadopoulos; B. Reifenhauser; F. Scheck SCALAR MATTER FIELD IN A FIXED POINT COMPACTIFIED FIVE-DIMENSIONAL KALUZA-KLEIN THEORY, Nuclear Physics B, Volume 281 (1987), pp. 426-444 | Article | MR: 869560

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[7] N. Papadopoulos; M. Paschke; A. Reyes; F. Scheck (In preparation)

[8] M. Paschke Von Nichtkommutativen Geometrien, ihren Symmetrien und etwas Hochenergiephysik (2001) (Ph.D. thesis, Mainz University)

[9] A. Reyes (Ph.D. thesis (in preparation), Mainz University)

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