Skip to main content
Log in

Retarded Green Functions and Modified Dispersion Relations

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • 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.

    Article  MATH  ADS  Google Scholar 

  • Arteaga, D., Parentani, R., and Verdaguer, E. (2004b). Propagation in a thermal graviton background. Physical Review D 70, 044019.

    Article  MathSciNet  ADS  Google Scholar 

  • 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.

    ADS  Google Scholar 

  • Birrell, N. D. and Davies, P. C. W. (1982). Quantum Fields in Curved Space, Cambridge University Press, Cambridge, England.

    MATH  Google Scholar 

  • 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.

    ADS  Google Scholar 

  • Calzetta, E., Roura, A., and Verdaguer, E. (2003). Stochastic description for open quantum systems. Physica A 319, 188–212, quant-ph/0011097.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Chou, K.-C., Su, Z.-B., Hao, B.-L., and Yu, L. (1985). Equilibrium and nonequilibrium formalisms made unified. Physics Reports 118, 1–131.

    Article  MathSciNet  ADS  Google Scholar 

  • Das, A. (1997). Finite Temperature Field Theory, World Scientific, Singapore.

    Google Scholar 

  • 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.

    Article  MathSciNet  ADS  Google Scholar 

  • Helfer, A. D. (2003). Do black holes radiate? Reports of Progress in Physics 66, 943–1008, gr-qc/0304042.

    Article  MathSciNet  ADS  Google Scholar 

  • Hillery, M., O'Connell, R. F., Scully, M. O., and Wigner, E. P. (1984). Distribution functions in physics: Fundamentals. Physics Reports 106, 121–167.

    Article  MathSciNet  ADS  Google Scholar 

  • Jacobson, T. (1991). Black hole evaporation and ultrashort distances. Physical Review D 44, 1731–1739.

    Article  MathSciNet  ADS  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  MathSciNet  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Peskin, M. E. and Schroeder, D. V. (1998). An Introduction to Quantum Field Theory, Addison-Wesley, Reading, MA.

    Google Scholar 

  • Schwinger, J. S. (1961). Brownian motion of a quantum oscillator. Journal of Mathematical Physics 2, 407.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Unruh, W. G. (1976). Notes on black hole evaporation. Physical Review D 12, 870–892.

    ADS  Google Scholar 

  • Wald, R. M. (1994). Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, The University of Chicago Press, Chicago.

    MATH  Google Scholar 

  • Weinberg, S. (1995). The Quantum Theory of Fields: Vol. I. Foundations, Cambridge University Press, Cambridge.

    Google Scholar 

  • Weldon, H. A. (1983). Simple rules for discontinuities in finite-temperature field theory. Physical Review D 28, 2007–2015.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Daniel Arteaga.

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-005-8888-z

Keywords

Navigation