Abstract
In this Chapter we generalize the noncommutative description of Yang–Mills theory to topologically non-trivial gauge configurations.
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References
Atiyah, M.F., Bott, R.: The Yang-Mills equations over Riemann surfaces. Philos. Trans. Roy. Soc. London Ser. A 308, 523–615 (1983)
Bleecker, D.: Gauge Theory and Variational Principles. Addison-wesley, Reading (1981)
Chamseddine, A.H., Connes, A.: Universal formula for noncommutative geometry actions: Unifications of gravity and the standard model. Phys. Rev. Lett. 77, 4868–4871 (1996)
Chamseddine, A.H., Connes, A.: The spectral action principle. Commun. Math. Phys. 186, 731–750 (1997)
Boeijink, J., van Suijlekom, W.D.: The noncommutative geometry of Yang-Mills fields. J. Geom. Phys. 61, 1122–1134 (2011)
Ćaćić, B.: A reconstruction theorem for almost-commutative spectral triples. Lett. Math. Phys. 100, 181–202 (2012)
Ćaćić, B.: Real structures on almost-commutative spectral triples. Lett. Math. Phys. 103, 793–816 (2013)
Boeijink. J., van den Dungen, K.: Notes on topologically non-trivial almost-commutative geometries. Work in progress
Serre, J.-P.: Modules projectifs et espaces fibrés à fibre vectorielle. In: Séminaire P. Dubreil, M.-L. Dubreil-Jacotin et C. Pisot, 1957/58, Fasc. 2, Exposé 23, p. 18. Secrétariat mathématique, Paris (1958)
Swan, R.G.: Vector bundles and projective modules. Trans. Am. Math. Soc. 105, 264–277 (1962)
Connes, A.: Non-commutative geometry and physics. In: Gravitation et quantifications (Les Houches, 1992), pp 805–950. North-Holland, Amsterdam (1995)
Landi, G.: An Introduction to Noncommutative Spaces and their Geometry. Springer, New York (1997)
Gracia-Bondía, J.M., Várilly, J.C., Figueroa, H.: Elements of Noncommutative Geometry. Birkhäuser, Boston (2001)
Dixmier, J., Douady, A.: Champs continus d’espaces hilbertiens et de \(C^{\ast } \)-algèbres. Bull. Soc. Math. France 91, 227–284 (1963)
Raeburn, I., Williams, D.P.: Morita Equivalence and Continuous-trace \(C^*\)-algebras, Volume 60 of Mathematical Surveys and Monographs. American Mathematical Society, Providence (1998)
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van Suijlekom, W.D. (2015). The Noncommutative Geometry of Yang–Mills Fields. In: Noncommutative Geometry and Particle Physics. Mathematical Physics Studies. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9162-5_10
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DOI: https://doi.org/10.1007/978-94-017-9162-5_10
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