Quantum Field Theory for Legspinners

  • Prakash Panangaden
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7860)


The notion of a particle in quantum field theory is dependent on the observer. This fundamental ambiguity in the definition of what seems a basic “objectively” observable concept is unsettling. In this short note I will survey the basics of field quantization and then discuss the Unruh effect which illustrates this phenomenon. I will describe an abstract version of quantum field theory in which a single mathematical object, a complex structure, captures all the ambiguity in the definition of a particle. There is nothing original in this paper, however, this particular presentation is not easy to extract from the extant literature and seems not be be known as widely as it deservers.


  1. 1.
    Woodhouse, N.M.J.: Introduction to analytical dynamics. Oxford University Press (1987)Google Scholar
  2. 2.
    Woodhouse, N.M.J.: Geometric Quantization, 2nd edn. Clarendon Press (1997)Google Scholar
  3. 3.
    Geroch, R.: Lectures on geometric quantum mechanics. Mimeographed notesGoogle Scholar
  4. 4.
    Marsden, J.E., Ratiu, T.: Introduction to Mechanics and Symmetry. Texts in Applied Mathematics, vol. 17. Springer (1994)Google Scholar
  5. 5.
    Geroch, R.: Mathematical Physics. Chicago Lectures in Physics. University of Chicago Press (1985)Google Scholar
  6. 6.
    Geroch, R.: Lectures on quantum field theory. Mimeographed notes (1971)Google Scholar
  7. 7.
    Baez, J., Segal, I.E., Zhou, Z.: Introduction to Algebraic and Constructive Quantum Field Theory. Princeton University Press (1992)Google Scholar
  8. 8.
    Ashtekar, A., Magnon, A.: Quantum fields in curved space-times. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 346(1646), 375–394 (1975)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Panangaden, P.: Positive and negative frequency decompositions in curved spacetimes. J. Math. Phys. 20, 2506–2510 (1979)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Parker, L.: Particle creation in expanding universes. Phys. Rev. Lett. 21, 562–564 (1968)CrossRefGoogle Scholar
  11. 11.
    Unruh, W.G.: Notes on black hole evaporation. Phys. Rev. D 14, 870–892 (1976)CrossRefGoogle Scholar
  12. 12.
    Fulling, S.A.: Nonuniqueness of canonical field quantization in riemannian space-time. Phys. Rev. D 7(10), 2850–2862 (1973)CrossRefGoogle Scholar
  13. 13.
    Davies, P.C.W.: Scalar particle production in schwarzschild and rindler metrics. J. Phys. A 8(4), 609–616 (1975)CrossRefGoogle Scholar
  14. 14.
    Unruh, W.G., Wald, R.M.: What happens when an accelerating observer detects a rindler particle. Phys. Rev. D 29(6), 1047–1056 (1984)CrossRefGoogle Scholar
  15. 15.
    Crispino, L., Higuchi, A., Matsas, G.: The unruh effect and its applications. Reviews of Modern Physics 80(3), 787 (2008)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Baez, J.: Notes on geometric quantization. Available on Baez’ web siteGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Prakash Panangaden
    • 1
  1. 1.School of Computer ScienceMcGill UniversityMontréalCanada

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