Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 9 (2013), 019, 22 pages      arXiv:1204.6268      https://doi.org/10.3842/SIGMA.2013.019

The Unruh Effect in General Boundary Quantum Field Theory

Daniele Colosi a and Dennis Rätzel b
a) Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Campus Morelia, C.P. 58190, Morelia, Michoacán, Mexico
b) Albert Einstein Institute, Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, 14476 Golm, Germany

Received November 07, 2012, in final form February 24, 2013; Published online March 02, 2013

Abstract
In the framework of the general boundary formulation (GBF) of scalar quantum field theory we obtain a coincidence of expectation values of local observables in the Minkowski vacuum and in a particular state in Rindler space. This coincidence could be seen as a consequence of the identification of the Minkowski vacuum as a thermal state in Rindler space usually associated with the Unruh effect. However, we underline the difficulty in making this identification in the GBF. Beside the Feynman quantization prescription for observables that we use to derive the coincidence of expectation values, we investigate an alternative quantization prescription called Berezin-Toeplitz quantization prescription, and we find that the coincidence of expectation values does not exist for the latter.

Key words: quantum field theory; Unruh effect; general boundary formulation.

pdf (499 kb)   tex (32 kb)

References

  1. Ashtekar A., Magnon A., Quantum fields in curved space-times, Proc. Roy. Soc. London Ser. A 346 (1975), 375-394.
  2. Belinski V.A., Quantum fields in black hole space-time and in accelerated systems, AIP Conf. Proc. 910 (2007), 270-293.
  3. Belinskii V.A., Karnakov B.M., Mur V.D., Narozhnyi N.B., Does the Unruh effect exist?, JETP Lett. 65 (1997), 902-908.
  4. Bell J., Leinaas J., Electrons as accelerated thermometers, Nuclear Phys. B 212 (1983), 131-150.
  5. Brout R., Massar S., Parentani R., Spindel P., A primer for black hole quantum physics, Phys. Rep. 260 (1995), 329-446, arXiv:0710.4345.
  6. Buchholz D., Solveen C., Unruh effect and the concept of temperature, arXiv:1212.2409.
  7. Colosi D., General boundary quantum field theory in de Sitter spacetime, arXiv:1010.1209.
  8. Colosi D., On the structure of the vacuum state in general boundary quantum field theory, arXiv:0903.2476.
  9. Colosi D., S-matrix in de Sitter spacetime from general boundary quantum field theory, arXiv:0910.2756.
  10. Colosi D., The general boundary formulation of quantum theory and its relevance for the problem of quantum gravity, AIP Conf. Proc. 1396 (2011), 109-113.
  11. Colosi D., Dohse M., On the structure of the S-matrix in general boundary quantum field theory in curved space, arXiv:1011.2243.
  12. Colosi D., Dohse M., Oeckl R., S-matrix for AdS from general boundary QFT, J. Phys. Conf. Ser. 360 (2012), 012012, 4 pages, arXiv:1112.2225.
  13. Colosi D., Oeckl R., S-matrix at spatial infinity, Phys. Lett. B 665 (2008), 310-313, arXiv:0710.5203.
  14. Colosi D., Oeckl R., Spatially asymptotic S-matrix from general boundary formulation, Phys. Rev. D 78 (2008), 025020, 22 pages, arXiv:0802.2274.
  15. Colosi D., Oeckl R., States and amplitudes for finite regions in a two-dimensional Euclidean quantum field theory, J. Geom. Phys. 59 (2009), 764-780, arXiv:0811.4166.
  16. Crispino L.C.B., Higuchi A., Matsas G.E.A., The Unruh effect and its applications, Rev. Modern Phys. 80 (2008), 787-838, arXiv:0710.5373.
  17. Earman J., The Unruh effect for philosophers, Stud. Hist. Philos. Sci. B Stud. Hist. Philos. Modern Phys. 42 (2011), 81-97.
  18. Erdélyi A., Magnus W., Oberhettinger F., Tricomi F.G., Higher transcendental functions, Vol. 1, McGraw-Hill, 1953.
  19. Fedotov A.M., Mur V.D., Narozhnyi N.B., Belinskii V.A., Karnakov B.M., Quantum field aspect of Unruh problem, Phys. Lett. A 254 (1999), 126-132, hep-th/9902091.
  20. Fell J.M.G., The dual spaces of C*-algebras, Trans. Amer. Math. Soc. 94 (1960), 365-403.
  21. Fulling S.A., Nonuniqueness of canonical field quantization in Riemannian space-time, Phys. Rev. D 7 (1973), 2850-2862.
  22. Fulling S.A., Unruh W.G., Comment on "Boundary conditions in the Unruh problem", Phys. Rev. D 70 (2004), 048701, 4 pages.
  23. Ginzburg V.L., Frolov V.P., Vacuum in a homogeneous gravitational field and excitation of a uniformly accelerated detector, Sov. Phys. Usp. 30 (1987), 1073-1095.
  24. Gradshteyn I.S., Ryzhik I.M., Table of integrals, series, and products, Academic Press, New York, 1980.
  25. Matsas G.E.A., Vanzella D.A.T., Decay of protons and neutrons induced by acceleration, Phys. Rev. D 59 (1999), 094004, 9 pages, gr-qc/9901008.
  26. Narozhny N.B., Fedotov A.M., Karnakov B.M., Mur V.D., Belinskii V.A., Boundary conditions in the Unruh problem, Phys. Rev. D 65 (2002), 025004, 23 pages, hep-th/9906181.
  27. Narozhny N.B., Fedotov A.M., Karnakov B.M., Mur V.D., Belinskii V.A., Quantum fields in accelerated frames, Ann. Phys. 9 (2000), 199-206.
  28. Narozhny N.B., Fedotov A.M., Karnakov B.M., Mur V.D., Belinskii V.A., Reply to "Comment on 'Boundary conditions in the Unruh problem"', Phys. Rev. D 70 (2004), 048702, 6 pages.
  29. Oeckl R., A "general boundary" formulation for quantum mechanics and quantum gravity, Phys. Lett. B 575 (2003), 318-324, hep-th/0306025.
  30. Oeckl R., Affine holomorphic quantization, J. Geom. Phys. 62 (2012), 1373-1396, arXiv:1104.5527.
  31. Oeckl R., General boundary quantum field theory: foundations and probability interpretation, Adv. Theor. Math. Phys. 12 (2008), 319-352, hep-th/0509122.
  32. Oeckl R., General boundary quantum field theory: timelike hypersurfaces in the Klein-Gordon theory, Phys. Rev. D 73 (2006), 065017, 13 pages, hep-th/0509123.
  33. Oeckl R., Holomorphic quantization of linear field theory in the general boundary formulation, SIGMA 8 (2012), 050, 31 pages, arXiv:1009.5615.
  34. Oeckl R., Observables in the general boundary formulation, in Quantum Field Theory and Gravity (Regensburg, 2010), Birkhäuser, Basel, 2012, 137-156, arXiv:1101.0367.
  35. Oeckl R., Probabilites in the general boundary formulation, J. Phys. Conf. Ser. 67 (2007), 012049, 6 pages, hep-th/0612076.
  36. Oeckl R., Schrödinger-Feynman quantization and composition of observables in general boundary quantum field theory, arXiv:1201.1877.
  37. Oeckl R., States on timelike hypersurfaces in quantum field theory, Phys. Lett. B 622 (2005), 172-177, hep-th/0505267.
  38. Oeckl R., The Schrödinger representation and its relation to the holomorphic representation in linear and affine field theory, J. Math. Phys. 53 (2012), 072301, 30 pages, arXiv:1109.5215.
  39. Oeckl R., Two-dimensional quantum Yang-Mills theory with corners, J. Phys. A: Math. Theor. 41 (2008), 135401, 20 pages, hep-th/0608218.
  40. Sciama D.W., Candelas P., Deutsch D., Quantum field theory, horizons and thermodynamics, Adv. Phys. 30 (1981), 327-366.
  41. Sewell G., Quantum fields on manifolds: PCT and gravitationally induced thermal states, Ann. Physics 141 (1982), 201-224.
  42. Takagi S., Vacuum noise and stress induced by uniform acceleration - Hawking-Unruh effect in Rindler manifold of arbitrary dimension, Progr. Theoret. Phys. Suppl. (1986), no. 88, 142 pages.
  43. Unruh W.G., Notes on black-hole evaporation, Phys. Rev. D 14 (1976), 870-892.
  44. Unruh W.G., Wald R.M., What happens when an accelerating observer detects a Rindler particle, Phys. Rev. D 29 (1984), 1047-1056.
  45. Unruh W.G., Weiss N., Acceleration radiation in interacting field theories, Phys. Rev. D 29 (1984), 1656-1662.
  46. Verch R., Local definiteness, primarity and quasiequivalence of quasifree Hadamard quantum states in curved spacetime, Comm. Math. Phys. 160 (1994), 507-536.
  47. Wald R.M., Quantum field theory in curved spacetime and black hole thermodynamics, Chicago Lectures in Physics, University of Chicago Press, Chicago, IL, 1994.

Previous article  Next article   Contents of Volume 9 (2013)