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.

DOI : 10.5802/ambp.193
Papadopoulos, Nikolaos A. 1 ; Paschke, Mario 2 ; Reyes, Andrés 1 ; Scheck, Florian 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
@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, Tome 11 (2004) no. 2, pp. 205-220. doi : 10.5802/ambp.193. http://www.numdam.org/articles/10.5802/ambp.193/

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

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

[4] Heil, A.; Papadopoulos, N.A.; Reifenhauser, B.; Scheck, F. 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] Laidlaw, M.G.G.; DeWitt, C.M. Feynman Functional Integrals for Systems of Indistinguishable Particles, Phys. Rev. D, Volume 3 (1971), pp. 1375-1378 | DOI

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

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

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

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

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

Cité par Sources :