Abstract
We analyse a three-field model, which describes a relativistic two-level atom interactingwith a radiation bath. From the one-loop retarded propagators at finite temperature we extract the transition rates and the modifications of the dispersion relations. To further investigate the relationships between propagators and these physical quantities, we analyse a non-equilibrium situation in which an additional atom is present in the bath. Preliminary results indicate that transition rates can still be extracted from the (retarded) propagator. This approach couldtherefore be useful in relating high-frequency (trans-Planckian) dispersion relations to the physical processes occurring at these scales.
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Arteaga, D., Parentani, R., and Verdaguer, E. (2004a). Gravity-mediated modifications of the dispersion relation in nontrivial backgrounds. International Journal of Theoretical Physics 43, 731–747.
Arteaga, D., Parentani, R., and Verdaguer, E. (2004b). Propagation in a thermal graviton background. Physical Review D 70, 044019.
Bedaque, P. F., Das, A. K., and Naik, S. (1997). Cutting rules at finite temperature. Modern Physics Letters A 12, 2481–2496, hep-ph/9603325.
Birrell, N. D. and Davies, P. C. W. (1982). Quantum Fields in Curved Space, Cambridge University Press, Cambridge, England.
Brout, R., Massar, S., Parentani, R., and Spindel, P. (1995). Hawking radiation without trans-Planckian frequencies. Physical Review D 52, 4559–4568, hep-th/9506121.
Calzetta, E., Roura, A., and Verdaguer, E. (2003). Stochastic description for open quantum systems. Physica A 319, 188–212, quant-ph/0011097.
Chou, K.-C., Su, Z.-B., Hao, B.-L., and Yu, L. (1985). Equilibrium and nonequilibrium formalisms made unified. Physics Reports 118, 1–131.
Das, A. (1997). Finite Temperature Field Theory, World Scientific, Singapore.
Donoghue, J. F., Holstein, B. R., and Robinett, R. W. (1985). Renormalization and radiative corrections at finite temperature. Annals of Physics (New York) 164, 233.
Helfer, A. D. (2003). Do black holes radiate? Reports of Progress in Physics 66, 943–1008, gr-qc/0304042.
Hillery, M., O'Connell, R. F., Scully, M. O., and Wigner, E. P. (1984). Distribution functions in physics: Fundamentals. Physics Reports 106, 121–167.
Jacobson, T. (1991). Black hole evaporation and ultrashort distances. Physical Review D 44, 1731–1739.
Keldysh, L. V. (1965). Diagram technique for nonequilibrium processes. Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki 47, 1515 (Sov. Phys. JETP 20, 1018).
le Bellac, M. (1996). Thermal Field Theory, Cambridge University Press, Cambridge, England.
Landsman, N. P. and van Weert, C. G. (1987). Real- and imaginary-time field theory at finite temperature and density. Physics Reports 145, 141–249.
Martin, J. and Brandenberger, R. H. (2001). The trans-Planckian problem of inflationary cosmology. Physical Review D 63, 123501, (http://arXiv.org/abs)hep-th/0005209.
Niemeyer, J. C. and Parentani, R. (2001). Trans-Planckian dispersion and scale-invariance of inflationary perturbations. Physical Review D 64, 101301, (http://arXiv.org/abs)astro-ph/0101451.
Parentani, R. (1995). The recoils of the accelerated detector and the decoherence of its fluxes. Nuclear Physics B 454, 227–249, gr-qc/9502030.
Peskin, M. E. and Schroeder, D. V. (1998). An Introduction to Quantum Field Theory, Addison-Wesley, Reading, MA.
Schwinger, J. S. (1961). Brownian motion of a quantum oscillator. Journal of Mathematical Physics 2, 407.
Unruh, W. G. (1976). Notes on black hole evaporation. Physical Review D 12, 870–892.
Wald, R. M. (1994). Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, The University of Chicago Press, Chicago.
Weinberg, S. (1995). The Quantum Theory of Fields: Vol. I. Foundations, Cambridge University Press, Cambridge.
Weldon, H. A. (1983). Simple rules for discontinuities in finite-temperature field theory. Physical Review D 28, 2007–2015.
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Arteaga, D., Parentani, R. & Verdaguer, E. Retarded Green Functions and Modified Dispersion Relations. Int J Theor Phys 44, 1665–1689 (2005). https://doi.org/10.1007/s10773-005-8888-z
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DOI: https://doi.org/10.1007/s10773-005-8888-z