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Modular Conjugation and the Implementation of Supersymmetry

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Abstract

Any \(\mathbb{Z}_{2}\)-graded C *-dynamical system with a self-adjoint graded-Kubo-Martin-Schwinger (KMS) functional on it can be represented (canonically) as a \(\mathbb{Z}_{2}\)-graded algebra of bounded operators on a \(\mathbb{Z}_{2}\)-graded Hilbert space, so that the grading of the latter is compatible with the functional. The modular conjugation operator plays a crucial role in this reconstruction. The results are generalized to the case of an unbounded graded-KMS functional having as dense domain the union of a net of C *-subalgebras. It is shown that the modulus of such an unbounded graded-KMS functional is KMS.

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References

  1. Buchholz, D., Grundling, H.: Algebraic Supersymmetry: A case study, arXiv:math-ph/0604044 v1 20 Apr 2006

  2. Buchholz, D., Longo, R.: Graded KMS Functionals and the Breakdown of Supersymmetry. Adv. Theor. Math. Phys. 3, 615–626, Addendum 1909–1910 (1999)

  3. Connes A. (1998). Entire cyclic cohomology of Banach algebras and characters of θ-summable Fredholm modules. K-Theory 1: 519–548

    Article  MathSciNet  Google Scholar 

  4. Connes, A.: Noncommutative Geometry. Academic, New York (1994)

  5. Dixmier, J.: C *-Algebras. North-Holland, Amsterdam (1977)

  6. Dixmier, J.: Von Neumann Algebras. North-Holland, Amsterdam (1981)

  7. Haag, R.: Local Quantum Physics. Springer, Berlin Heidelberg New York (1992)

  8. Jaffe A., Lesniewski A. and Osterwalder K. (1989). Super-KMS functionals and entire cyclic cohomology. K-Theory 2(6): 675–682

    Article  MATH  MathSciNet  Google Scholar 

  9. Jaffe A., Lesniewski A. and Osterwalder K. (1988). Quantum K-theory I. Commun. Math. Phys. 118: 1–14

    Article  MATH  ADS  MathSciNet  Google Scholar 

  10. Kastler D. (1989). Cyclic cocycles from graded KMS functionals. Commun. Math. Phys. 121: 345–350

    Article  ADS  MathSciNet  Google Scholar 

  11. Kastler, D.: Cyclic cohomology, supersymmetry and KMS states. The KMS states as generalized elliptic operators, Preprint CPT-89/P.2280. May 1989.

  12. Longo R. (2001). Notes for a Quantum Index Theorem. Commun. Math. Phys. 222: 45–96

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. Pedersen, G.: C *-Algebras and Their Automorphism Groups. Academic, New York (1979)

  14. Sakai S. (1958). On linear functionals of W *-algebras. Proc. Japan Acad. 34: 571–574

    Article  MATH  MathSciNet  Google Scholar 

  15. Stoytchev O. (1993). The modular group and super-KMS functionals. Lett. Math. Phys. 27: 43–50

    MATH  MathSciNet  ADS  Google Scholar 

  16. Witten E. (1982). Constraints on supersymmetry breaking. Nucl. Phys. B 202: 253

    Article  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. American University in Bulgaria, 2700, Blagoevgrad, Bulgaria

    Orlin Stoytchev

  2. Institute for Nuclear Research, 1784, Sofia, Bulgaria

    Orlin Stoytchev

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  1. Orlin Stoytchev
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Correspondence to Orlin Stoytchev.

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Stoytchev, O. Modular Conjugation and the Implementation of Supersymmetry. Lett Math Phys 79, 235–249 (2007). https://doi.org/10.1007/s11005-006-0132-0

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  • DOI: https://doi.org/10.1007/s11005-006-0132-0

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