# The spin-statistics relation in nonrelativistic quantum mechanics and projective modules

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

Annales mathématiques Blaise Pascal (2004)

- Volume: 11, Issue: 2, page 205-220
- ISSN: 1259-1734

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topPapadopoulos, Nikolaos A., et al. "The spin-statistics relation in nonrelativistic quantum mechanics and projective modules." Annales mathématiques Blaise Pascal 11.2 (2004): 205-220. <http://eudml.org/doc/10506>.

@article{Papadopoulos2004,

abstract = {In this work we consider non-relativistic quantum mechanics, obtained from a classical configuration space $\mathcal\{Q\}$ of indistinguishable particles. Following an approach proposed in [8], wave functions are regarded as elements of suitable projective modules over $C(\mathcal\{Q\})$. 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.},

affiliation = {Johannes-Gutenberg-Universität Institut für Physik - ThEP. Staudinger Weg 7 Mainz, D-55128 Germany; Max Planck Institute for Mathematics in the Sciences Inselstrasse 22-26 Leipzig, D-04103 Germany; Johannes-Gutenberg-Universität Institut für Physik - ThEP. Staudinger Weg 7 Mainz, D-55128 Germany; Johannes-Gutenberg-Universität Institut für Physik - ThEP. Staudinger Weg 7 Mainz, D-55128 Germany},

author = {Papadopoulos, Nikolaos A., Paschke, Mario, Reyes, Andrés, Scheck, Florian},

journal = {Annales mathématiques Blaise Pascal},

language = {eng},

month = {7},

number = {2},

pages = {205-220},

publisher = {Annales mathématiques Blaise Pascal},

title = {The spin-statistics relation in nonrelativistic quantum mechanics and projective modules},

url = {http://eudml.org/doc/10506},

volume = {11},

year = {2004},

}

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

DA - 2004/7//

PB - Annales mathématiques Blaise Pascal

VL - 11

IS - 2

SP - 205

EP - 220

AB - In this work we consider non-relativistic quantum mechanics, obtained from a classical configuration space $\mathcal{Q}$ of indistinguishable particles. Following an approach proposed in [8], wave functions are regarded as elements of suitable projective modules over $C(\mathcal{Q})$. 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.

LA - eng

UR - http://eudml.org/doc/10506

ER -

## References

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- N. Papadopoulos, M. Paschke, A. Reyes, F. Scheck
- M. Paschke, Von Nichtkommutativen Geometrien, ihren Symmetrien und etwas Hochenergiephysik, (2001)
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