We present a formal derivation of the Mino–Sasaki–Tanaka–Quinn–Wald (MSTQW) equation describing the self-force on a (semi-) classical relativistic point mass moving under the influence of quantized linear metric perturbations on a curved background space–time. The curvature of the space–time implies that the dynamics of the particle and the field is history-dependent and as such requires a non-equilibrium formalism to ensure the consistent evolution of both particle and field, viz., the worldline influence functional and the closed- time-path (CTP) coarse-grained effective action. In the spirit of effective field theory, we regularize the formally divergent self-force by smearing the local part of the retarded Green’s function and employing a quasi-local expansion. We derive the MSTQW–Langevin equations describing the perturbations of the particle’s worldline about its semi-classical trajectory resulting from interactions with the quantum fluctuations of the linear metric perturbations. Finally, we demonstrate that the quantum fluctuations of the field could, in principle, leave imprints on gravitational waveforms expected to be observed by gravitational interferometers, thereby encoding information about tree-level perturbative quantum gravity.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abramovici A. et al. (1992). Science 256: 325
The LISA website is http://lisa.jpl.nasa.gov/.
L. Blanchet, Phys. Rev. D 54, 1417 (1996); 71, 129904(E) (2005); L. Blanchet, B. R. Iyer, and B. Joguet, Phys. Rev. D 65, 064005 (2002); 71, 129903(E) (2005); L. Blanchet, G. Faye, B. R. Iyer, and B. Joguet, Phys. Rev. D 65, 061501 (2002); 71, 129902(E) (2005).
P. Jaranowski and G. Schäfer, Phys. Rev. D 57, 7274 (1998); 63, 029902(E) (2001); 60, 124003 (1999); T. Damour, P. Jaranowski, and G. Schafer, Phys. Rev. D 62, 021501 (2000); 63, 029903(E) (2001); 63, 044023 (2001); 72, 029902(E) (2005); L. Blanchet and G. Faye, Phys. Lett. A 271, 58 (2000); Phys. Rev. D 63, 062005 (2001); V. C. de Andrade, L. Blanchet, and G. Faye, Class. Quant. Gravit. 18, 753 (2001); L. Blanchet and B. R. Iyer, Class. Quant. Gravit. 20, 755 (2003).
Mino Y., Sasaki M., Tanaka T. (1997). Phys. Rev. D 55: 3457
Quinn T.C., Wald R.M. (1997). Phys. Rev. D 56: 3381
E. Poisson, “The motion of point particles in curved spacetime,” Living Rev. Relativity 7, 6 (2004). URL (cited on 26 March 2004): http://www.livingreviews.org/lrr-2004-6 [gr-qc/0306052].
P. Johnson and B. L. Hu, [quant-ph/0012137]; Phys. Rev. D 65, 065015 (2002).
P. R. Johnson and B. L. Hu, Found. Phys. 35, 1117 (2005), and references therein; P. Johnson, Ph. D. dissertation, University of Maryland (1999).
A. Raval, B. L. Hu, and J. Anglin, Phys. Rev. D 53, 7003 (1996); A. Raval, B. L. Hu, and D. Koks, Phys. Rev. D 55, 4795 (1997); A. Raval, Ph. D. dissertation, University of Maryland (1996).
Galley C.R., Hu B.L., Lin S.Y. (2006). Phys. Rev. D 74: 024017
Galley C.R., Hu B.L. (2005). Phys. Rev. D 72: 084023
Misner C.W., Thorne K.S., Wheeler J.A. (1973) Gravitation. Freeman, San Fransisco
P. A. M. Dirac, Lectures on Quantum Mechanics (Belfer Graduate School of Science, Yeshiva University, New York, 1964).
Faddeev L.D., Popov V.N. (1967). Phys. Lett. 25B: 29
Hu B.L., Paz J.P., Zhang Y. (1992). Phys. Rev. D 45: 2843
Grabert H., Schramm P., Ingold G.L. (1988). Phys. Rep. 168: 115
Romero L.D., Paz J.P. (1997). Phys. Rev. A 55: 4070
W. Goldberger and I. Z. Rothstein, Phys. Rev. D 73, 104029 (2006); R. A. Porto, Phys. Rev. D 73, 104031 (2006).
I. Z. Rothstein and R. A. Porto, Phys. Rev. Lett. 97, 021101 (2006).
P. R. Johnson and B. L. Hu, Found. Phys. 35, 1117 (2005) [gr-qc/0501029].
E. Calzetta and B. L. Hu, Phys. Rev. D 37, 2878 (1988).
R. B. Griffiths, J. Stat. Phys. 36, 219 (1984); R. Omnès, J. Stat Phys. 53, 893 (1988); ibid. 53, 933 (1988); ibid. 53, 957 (1988); ibid. 57, 357 (1988); Ann. Phys. (NY) 201, 354 (1990); Rev. Mod. Phys. 64, 339 (1992); The Interpretation of Quantum Mechanics (Princeton UP, Princeton, 1994); M. Gell-Mann and J. B. Hartle, in Complexity, Entropy and the Physics of Information, W. H. Zurek, ed. (Addison-Wesley, Reading, 1990); M. Gell-Mann and J. B. Hartle, Phys. Rev. D 47, 3345 (1993); J. B. Hartle, “Quantum mechanics of closed systems,” in Directions in General Relativity, Vol. 1, B. L. Hu, M. P. Ryan, and C. V. Vishveswara eds. (Cambridge University, Cambridge, 1993); H. F. Dowker and J. J. Halliwell, Phys. Rev. D 46, 1580 (1992); J. J. Halliwell, Phys. Rev. D 48, 4785 (1993); ibid. 57, 2337 (1998); T. A. Brun, Phys. Rev. D 47, 3383 (1993); J. P. Paz and W. H. Zurek, Phys. Rev. D 48, 2728 (1993); J. Twamley, Phys. Rev. D 48, 5730 (1993).
E. Calzetta and B. L. Hu, “Decoherence of correlation histories,” in Directions in General Relativity, Vol. 2, B. L. Hu and T. A. Jacobson, eds. (Cambridge University, Cambridge, 1993), pp. 38–65.
Hadamard J. (1923) Lectures on Cauchy’s Problem. Yale University Press, New Haven
P. Johnson and B. L. Hu, [quant-ph/0012137] (2000); P. R. Johnson and B. L. Hu, Phys. Rev. D 65, 065015 (2002).
Schutz B.F. (1985) A First Course in General Relativity. (Cambridge University Press, Cambridge, UK
Calzetta E., Roura A., Verdaguer E. (2003). Physica A (Amsterdam) 319: 188
D. A. R. Dalvit and F. D. Mazzitelli, Phys. Rev. D 56, 7779 (1997); D. A. R. Dalvit and F. D. Mazzitelli, Phys. Rev. D 60, 084018 (1999).
Author information
Authors and Affiliations
Corresponding author
Additional information
Invited talk given at the International Association for Relativistic Dynamics (IARD),June 2006, University of Connecticut.
Rights and permissions
About this article
Cite this article
Galley, C.R. Gravitational Self-force from Quantized Linear Metric Perturbations in Curved Space. Found Phys 37, 460–479 (2007). https://doi.org/10.1007/s10701-007-9111-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-007-9111-2