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Annales Henri Poincaré

, Volume 18, Issue 8, pp 2693–2714 | Cite as

Global Anomalies on Lorentzian Space-Times

  • Alexander Schenkel
  • Jochen Zahn
Article
  • 57 Downloads

Abstract

We formulate an algebraic criterion for the presence of global anomalies on globally hyperbolic space-times in the framework of locally covariant field theory. We discuss some consequences and check that it reproduces the well-known global SU(2) anomaly in four space-time dimensions.

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Notes

Acknowledgements

We would like to thank Dirk-André Deckert, Chris Fewster, Stefan Hollands and Ko Sanders for helpful discussions. A.S. was supported by a Research Fellowship of the Deutsche Forschungsgemeinschaft (DFG, Germany). A large part of the work presented here was done at Heriot-Watt University Edinburgh. J.Z. would like to thank the Department of Mathematics for the kind hospitality and the COST action “Quantum structure of spacetime(QSPACE)” for funding the visit through the “short term scientific missions” program.

References

  1. 1.
    Witten, E.: An SU(2) anomaly. Phys. Lett. B 117, 324 (1982)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Nelson, P.C., Alvarez-Gaume, L.: Hamiltonian interpretation of anomalies. Commun. Math. Phys. 99, 103 (1985)ADSMathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Jackiw, R.: Topological investigations of quantized gauge theories. In: Stora, R., DeWitt, B. (eds.) Relativity, Groups and Topology II. North-Holland, Amsterdam (1986)Google Scholar
  4. 4.
    Ruijsenaars, S.N.M.: Charged particles in external fields. 1. Classical theory. J. Math. Phys. 18, 720 (1977)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Brunetti, R., Fredenhagen, K., Verch, R.: The generally covariant locality principle: a New paradigm for local quantum field theory. Commun. Math. Phys. 237, 31 (2003). [arXiv:math-ph/0112041]
  6. 6.
    Hollands, S., Wald, R.M.: Local Wick polynomials and time ordered products of quantum fields in curved space-time. Commun. Math. Phys. 223, 289 (2001). [arXiv:gr-qc/0103074]
  7. 7.
    Zahn, J.: The renormalized locally covariant Dirac field. Rev. Math. Phys. 26(1), 1330012 (2014). [arXiv:1210.4031 [math-ph]]MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Fewster, C.J., Verch, R.: Dynamical locality and covariance: what makes a physical theory the same in all spacetimes? Ann. Henri Poincaré 13, 1613 (2012). [arXiv:1106.4785 [math-ph]]ADSMathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Hollands, S., Wald, R.M.: Conservation of the stress tensor in interacting quantum field theory in curved spacetimes. Rev. Math. Phys. 17, 227 (2005). [arXiv:gr-qc/0404074]MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Zahn, J.: Locally covariant charged fields and background independence. Rev. Math. Phys. 27(07), 1550017 (2015). [arXiv:1311.7661 [math-ph]]MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Witten, E.: Global aspects of current algebra. Nucl. Phys. B 223, 422 (1983)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    Elitzur, S., Nair, V.P.: Nonperturbative anomalies in higher dimensions. Nucl. Phys. B 243, 205 (1984)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Sanders, K.: Essential self-adjointness of Wick squares in quasi-free Hadamard representations on curved spacetimes. J. Math. Phys. 53, 042502 (2012). [arXiv:1010.3978 [math-ph]]ADSMathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Fewster, C.J.: Endomorphisms and automorphisms of locally covariant quantum field theories. Rev. Math. Phys. 25, 1350008 (2013). [arXiv:1201.3295 [math-ph]]MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Bogoliubov, N.N., Shirkov, D.V.: Introduction to the Theory of Quantized Fields, 3rd edn. Wiley, New York (1980)Google Scholar
  16. 16.
    Scharf, G.: Finite Quantum Electrodynamics, 2nd edn. Springer, Berlin (1995)CrossRefMATHGoogle Scholar
  17. 17.
    Scharf, G., Wreszinski, W.F.: The causal phase in quantum electrodynamics. Nuovo Cim. A 93, 1 (1986)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Gracia-Bondia, J.M.: The phase of the scattering matrix. Phys. Lett. B 482, 315 (2000). [arXiv:hep-th/0003141]
  19. 19.
    Alvarez-Gaume, L., Witten, E.: Gravitational anomalies. Nucl. Phys. B 234, 269 (1984)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Elitzur, S., Frishman, Y., Rabinovici, E., Schwimmer, A.: Origins of global anomalies in quantum mechanics. Nucl. Phys. B 273, 93 (1986)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    Wess, J., Zumino, B.: Consequences of anomalous Ward identities. Phys. Lett. B 37, 95 (1971)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Bardeen, W.A., Zumino, B.: Consistent and covariant anomalies in gauge and gravitational theories. Nucl. Phys. B 244, 421 (1984)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Zahn, J.: Locally covariant chiral fermions and anomalies. Nucl. Phys. B 890, 1 (2014). [arXiv:1407.1994 [hep-th]]ADSMathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of NottinghamNottinghamUK
  2. 2.Institut für Theoretische PhysikUniversität LeipzigLeipzigGermany

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