A Symplectic Approach to Yang Mills Theory for Non Commutative Tori
Canadian journal of mathematics, Tome 44 (1992) no. 2, pp. 368-387

Voir la notice de l'article provenant de la source Cambridge University Press

In this note we give a symplectic approach to Yang Mills theory for non commutative n-tori, inspired by the classical theory of Atiyah and Bott.
DOI : 10.4153/CJM-1992-025-9
Mots-clés : 46L55, 53C57, 81El3, 46E99 (46E35), 58B20
Spera, Mauro. A Symplectic Approach to Yang Mills Theory for Non Commutative Tori. Canadian journal of mathematics, Tome 44 (1992) no. 2, pp. 368-387. doi: 10.4153/CJM-1992-025-9
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[1] 1. Atiyah, M.F. and Bott, R., The Yang Mills Equations over Riemann Surfaces, Phil. Trans. R. Soc. London A 308(1982), 523–615. Google Scholar

[2] 2. Abraham, R. and Marsden, J.E., Foundations of Mechanics (2nd edition), Benjamin London, Amsterdam, 1978. Google Scholar

[3] 3. Connes, A., C* algebres et géométrie différentielle, C.R. Acad. Sci. Paris, Série I, 290( 1980), 599–604. Google Scholar

[4] 4. Connes, A., Non Commutative Differential Geometry, Publ. Math. IHES 62(1986), 41–144. Google Scholar

[5] 5. Connes, A., A Survey ofC* algebras of Foliations, Proc. Symp. Pure Math. 38, 1(1982), 521–628. Google Scholar

[6] 6. Connes, A. and Rieffel, M.A., Yang Mills for Non Commutative Two Tori, Proceedings of the Conference on Operator Algebras and Mathematical Physics, Univ. of Iowa, 1985 Contemporary Mathematics 62(1987), 237–266. Google Scholar

[7] 7. Dixmier, J., Sur la Relation i(PQ - QP)= /, Compos. Math. 13(1956), 263–269. Google Scholar

[8] 8. Donaldson, S.K., A New Proof of a Theorem ofNarasimhan and Seshadri, J. Diff. Geom. 18(1983), 269- 277. Google Scholar

[9] 9. Donaldson, S.K., Anti Self-dual Yang Mills Connections over Complex Algebraic Surfaces, Proc. London Math. Soc. 50(1985), 1–26. Google Scholar

[10] 10. Freed, D. and Uhlenbeck, K., Istantons on Four-Manifolds, Springer-Verlag Berlin, Heidelberg 1984. Google Scholar

[11] 11. Guillemin, V. and Sternberg, S., Geometric Quantization and Multiplicity of Group Representations, Inv. Math. 67(1982), 515–538. Google Scholar

[12] 12. Howe, R., On the role of the Heisenberg group in Harmonic Analysis, Bull. Am. Math. Soc. 3(1980), 822- 843. Google Scholar

[13] 13. Kirillov, A., Eléments de la Théorie des Représentations, MIR Publishers Moscow 1974. Google Scholar

[14] 14. Lawson, H.B., The theory of gauge fields in four dimensions, Reg. Conf. Ser. in Math 58 Providence, Rhode Island 1985. Google Scholar

[15] 15. Reed, M. and Simon, B., Methods of Modern Mathematical Physics, (Volumes I and II), Academic Press New York 1972–75. Google Scholar

[16] 16. Rieffel, M.A., Vector Bundles over Higher Dimensional Non Commutative Tori, Lecture Notes in Mathematics 1132, 456–467.Springer-Verlag, Berlin, Heidelberg, New York 1985. Google Scholar

[17] 17. Rieffel, M.A., Projective modules over higher dimensional non commutative tori, Canad. J. Math., (2) XL( 1988), 257–338. Google Scholar

[18] 18. Rieffel, M.A., Critical Points of Yang Mills for Non Commutative Two Tori, J. Diff. Geom. 31(1990), 535–546. Google Scholar

[19] 19. Spera, M., Quantum Mechanical Commutation Relations and Differential Geometry (Classical and Non Commutative), in Proceedings of the X° Open University Conference on Statistical Mechanics (Solomon, A. Ed.) World Scientific Press (1988), 74–100. Google Scholar

[20] 20. Spera, M., Yang Mills Equations and Holomorphic Structures on C*-dynamical Systems, Preprint (1988) (unpublished). Google Scholar

[21] 21. Spera, M., Yang Mills theory in non commutative differential geometry, Rend. Sem. Fac. Scienze Univ. Cagliari, Suppl. 58(1988), 409–421. Google Scholar

[22] 22. Spera, M., A Non Commutative Geometric Re interpretation of the Canonical Commutation Relations, Bollettino dell'Unione Matematica Italiana, 58(1991), 53–63. Google Scholar

[23] 23. Spera, M., Sobolev theory for non commutative tori, Rend. Sem. Mat. Univ. Padova (1991) (to appear). Google Scholar

[24] 24. Spera, M., A Note on Yang Mills Minima on Rieffel Modules over Higher Dimensional Non Commutative Tori, Preprint (1990). Google Scholar

[25] 25. von Neumann, J., Die Eindeutigkeit der Schrodingerschen Operatoren, Math. Ann. 104(1931), 570–578. Google Scholar

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