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Quantum Field Theory on Curved Spacetimes pp 1–37Cite as

C*-algebras

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Part of the book series: Lecture Notes in Physics ((LNP,volume 786))

Abstract

In this chapter we will collect those basic concepts and facts related to C*-algebras that will be needed later on. We give complete proofs. In Sects. 1, 2, 3, and 6 we follow closely the presentation in [1]. For more information on C*-algebras, see, e.g. [2–6].

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References

  1. Bär, C., Ginoux, N., Pfäffle, F.: Wave equations on Lorentzian manifolds and quantization. EMS Publishing House, Zürich (2007)

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  2. Bratteli, O., Robinson, D.W.: Operator Algebras and Quantum Statistical Mechanics I. Springer, Berlin Heidelberg (2002)

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  3. Davidson, K.: C_-algebras by example. AMS, Providence (1997)

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  4. Dixmier, J.: Les C*-algèbres et leurs représentations, 2nd edition, Gauthier-Villars Éditeur, Paris (1969)

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  5. Murphy, G.: C*-algebras and operator theory. Academic Press, Boston (1990)

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  6. Takesaki, M.: Theory of Operator Algebra I, Springer, Berlin, Heidelberg, New York (2002)

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  7. Manuceau, J.: C*-algèbre de relations de commutation. Ann. Inst. H. Poincaré Sect. A (N.S.) 8, 139 (1968)

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  8. Bratteli, O., Robinson, D.W.: Operator Algebras and Quantum Statistical Mechanics II. Springer, Berlin Heidelberg 2002

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  9. Baez, F.: Bell’s inequality for C*-Algebras. Lett. Math. Phys. 13(2), 135–136 (1987)

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Universität Potsdam, Am Neuen Palais 10, D-14469, Potsdam, Germany

    Christian Bär & Christian Becker

Authors
  1. Christian Bär
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  2. Christian Becker
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Corresponding author

Correspondence to Christian Bär .

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Editors and Affiliations

  1. Inst. Mathematik, Universität Potsdam, Potsdam, 14415, Germany

    Christian Bär

  2. Inst. Theoretische Physik II, Universität Hamburg, Luruper Chaussee 149, Hamburg, 22761, Germany

    Klaus Fredenhagen

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Bär, C., Becker, C. (2009). C*-algebras. In: Bär, C., Fredenhagen, K. (eds) Quantum Field Theory on Curved Spacetimes. Lecture Notes in Physics, vol 786. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02780-2_1

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  • DOI: https://doi.org/10.1007/978-3-642-02780-2_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02779-6

  • Online ISBN: 978-3-642-02780-2

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

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