Abstract
We propose a mode-sum formalism for the quantization of the scalar field based on distributional modes, which are naturally associated with a slight modification of the standard plane-wave modes. We show that this formalism leads to the standard Rindler temperature result, and that these modes can be canonically defined on any Cauchy surface.
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REFERENCES
Manogue, C. A., Dray, T., and Copeland, E. (1988). The Trousers Problem Revisited, Pramãna—J. Phys. 30, 279–292.
Fulling, S. A. (1989). Aspects of Quantum Field Theory in Curved Space-Time, Cambridge University Press, Cambridge.
Fischer, J. (1998). A New Look at the Ashtekar-Magnon Energy Condition, Ph.D. Dissertation, Oregon State University.
Fischer, J., and Dray, T. (1999). A New Look at the Ashtekar-Magnon Energy Condition, Gen. Rel. Grav. 31, 511.
Birrell, N. D., and Davies, P. C. W. (1982). Quantum Fields in Curved Space, Cambridge University Press, Cambridge.
Kay, B. S., Radzikowski, M. J., and Wald, R. M. (1997). Commun. Math. Phys. 183, 533.
Kay, B. S. (1996). Quantum Fields in Curved Spacetime: Non Global Hyperbolicity and Locality, in: Proceedings of the Conference Operator Algebras and Quantum Field Theory, eds. S. Doplicher, R. Longo, J. Roberts, L. Zsido, International Press, MA.
Hawking, S. W. (1992). Phys. Rev. D 46, 603.
Dray, T., and Manogue, C. A. (1988). Bogolubov Transformations and Completeness, Gen. Rel. Grav. 20, 957–965.
Roman, P. (1969). Introduction to Quantum Field Theory, Wiley, New York.
Dray, T., and Manogue, C. A. (1987). The Scalar Field in Curved Space, Institute of Mathematical Sciences report no. 112, Madras, 83 pages.
Unruh, W. (1976). Notes on Black Hole Evaporation, Phys. Rev. D 14, 870.
Wald, R. M. (1994). Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, University of Chicago Press, Chicago.
Dimock, J. (1980). Commun. Math. Phys. 77, 219.
Choquet-Bruhat, Y. (1968). Hyperbolic Differential Equations on a Manifold, in: Battelle Recontres: 1967 Lectures in Mathematics and Physics, eds. C. M. DeWitt and J. A. Wheeler, Benjamin, NY.
Boersma, S. and Dray, T. (1995). Slicing, Threading and Parametric Manifolds, Gen. Rel. Grav. 27, 319–339.
Agnew, A. F. (1999). Distributional Modes for Curved Space Quantum Field Theory, Ph.D. Dissertation, Oregon State University.
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Agnew, A.F., Dray, T. Distributional Modes for Scalar Field Quantization. General Relativity and Gravitation 33, 429–453 (2001). https://doi.org/10.1023/A:1010236506377
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DOI: https://doi.org/10.1023/A:1010236506377