Annales Mathématiques
Blaise Pascal
no. 2
The spin-statistics relation in nonrelativistic quantum mechanics and projective modules
Nikolaos A. Papadopoulos1 ; Mario Paschke2 ; Andrés Reyes1 ; Florian Scheck1
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.

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, Tome 11 (2004) no. 2, pp. 205-220. doi : 10.5802/ambp.193. https://ambp.centre-mersenne.org/articles/10.5802/ambp.193/

[1] M. F. Atiyah K-theory, Benjamin, New York, 1967 | MR

[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 | DOI | MR | Zbl

[3] M.V. Berry; J.M. Robbins Quantum indistinguishability: alternative constructions of the transported basis, J. Phys. A: Math. Gen., Volume 33 (2000), p. L207-L214 | DOI | MR | Zbl

[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 | DOI | MR

[5] M.G.G. Laidlaw; C.M. DeWitt Feynman Functional Integrals for Systems of Indistinguishable Particles, Phys. Rev. D, Volume 3 (1971), pp. 1375-1378 | DOI

[6] J.M. Leinaas; J. Myrheim On the Theory of Identical Particles, Nuovo Cim. B, Volume 37 (1977), pp. 1-23 | DOI

[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

[10] J. Sladkowski Generalized G-Theory, Int. J. Theor. Phys., Volume 30 (1991), pp. 517-520 | DOI

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