Abstract
We present a stochastic theory for the nonequilibriurn dynamics of charges moving in a quantum scalar field based on the worldline influence functional and the close-time-path (CTP or in-in) coarse-grained effective action method. We summarize (1) the steps leading to a derivation of a modified Abraham-Lorentz-Dirac equation whose solutions describe a causal semiclassical theory free of runaway solutions and without pre-acceleration patholigies, and (2) the transformation to a stochastic effective action, which generates Abraham-Lorentz-Dirac-Langevin equations depicting the fluctuations of a particle’s worldline around its semiclassical trajectory. We point out the misconceptions in trying to directly relate radiation reaction to vacuum fluctuations, and discuss how, in the framework that we have developed, an array of phenomena, from classical radiation and radiation reaction to the Unruh effect, are interrelated to each other as manifestations at the classical, stochastic and quantum levels. Using this method we give a derivation of the Unruh effect for the spacetime worldline coordinates of an accelerating charge. Our stochastic particle-field model, which was inspired by earlier work in cosmological backreaction, can be used as an analog to the black hole backreaction problem describing the stochastic dynamics of a black hole event horizon.
Similar content being viewed by others
References
P. R. Johnson, Ph.D. thesis, University of Maryland, College Park, 1999 (unpublished).
P. R. Johnson and B. L. Hu, Stochastic theory of relativistic particles moving in a quantum field: influence functional and Langevin equation [quant-ph/0012137].
E. B. Davies, The Quantum Theory of Open Systems (Academic, London, 1976); U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 1993).
A. O. Caldeira and A. J. Leggett, Physica A 121, 587 (1983); Ann. Phys. (N.Y.) 149, 374 (1983); A. J. Leggett et al. Rev. Mod. Phys. 59, 1 (1987); V. Hakim and V. Ambegaokar, Phys. Rev. A 32, 423 (1985); F. Haake and R. Reibold, Phys. Rev. A 32, 2462 (1985); H. Grabert, P. Schramm, and G. L. Ingold, Phys. Rep. 168, 115 (1988); B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992); D 47, 1576 (1993).
R. Feynman and F. Vernon, Ann. Phys. (N.Y.) 24, 118 (1963); R. Feynman and A. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
J. Schwinger, J. Math. Phys. 2, 407 (1961); L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964) [Sov. Phys. JETP 20, 1018 (1965)]; G. Zhou, Z.B. Su, B. Hao, and L. Yu, Phys. Rep. 118, 1 (1985); Z.B. Su, L. Y. Chen, X.T. Yu, and K.C. Chou, Phys. Rev. B 37, 9810 (1988); B. S. DeWitt, in Quantum Concepts in Space and Time, R. Penrose and C. J. Isham, eds. (Claredon, Oxford, 1986); R. D. Jordan, Phys. Rev. D 33, 444 (1986); E. Calzetta and B. L. Hu, Phys. Rev. D 35, 495 (1987); 37, 2878 (1988); 49, 6636 (1994); A. Campos and E. Verdaguer, Phys. Rev. D 49, 1861 (1994).
B. L. Hu and Y. Zhang, Coarse-graining, scaling, and inflation University of Maryland Preprint 90-186 (1990); B. L. Hu, in Relativity and Gravitation: Classical and Quantum, Proc. SILARG VII, Cocoyoc, Mexico 1990. J. C. D’ Olivo et al. eds. (World Scientific, Singapore, 1991); Sukanya Sinha and B. L. Hu, Phys. Rev. D 44, 1028 (1991); F. Lombardo and F. D. Mazzitelli, Phys. Rev. D 53, 2001 (1996).
E. A. Calzetta B.-L. Hu F. D. Mazzitelli (2001) Phys. Rep. 352 459–520 Occurrence Handle10.1016/S0370-1573(01)00043-6 Occurrence Handle2001PhR...352..459C Occurrence Handle2002i:83028
A. O. Barut and I. H. Duru, Phys. Rev. 172, 1 (1989); M.J. Strassler, Nucl. Phys. B 385, 145 (1992); D.G.C. McKeon, Ann. Phys. (N.Y.) 224, 139 (1993); M.J. Schmidt and C. Schubert, Phys. Rev. Lett. 331, 69 (1994); Phys. Lett. B 318, 438 (1993); H. Kleinert, Path Integrals in Quantum Mechanics, Statistical and Polymer Physics (World Scientific, London, 1995); D. Fliegner, M. G. Schmidt, and C. Schubert, Nucl. Phys. B 51C, 174 (1996); J. Jalilian-Marian et al., Phys. Rev. D 62, 045020 (2000); R. Venugopalan and J. Wirstam, Phys. Rev. D 63, 125022 (2001).
P.R. Johnson B.L. Hu (2002) Phys. Rev. 65 065015
W.G. Unruh (1976) Phys. Rev. 14 3251 Occurrence Handle1976PhRvD..14.3251U
B.S. DeWitt (1975) Phys Rep. D 19 297 Occurrence Handle1975PhR....19..295D
B. L. Hu, in Proceedings of the Third International Workshop on Thermal Fields and its Applications, CNRS Summer Institute, Banff, August 1993, R. Kobes and G. Kunstatter, eds. (World Scientific, Singapore, 1994) [gr-qc/9403061]; Yuhong Zhang, Ph.D. Thesis, University of Maryland 1990 (unpublished).
S. A. Ramsey and B. L. Hu, Phys. Rev. D 56, 678 (1997); S. A. Ramsey, B. L. Hu, and A. M. tylianopoulos, Phys. Rev. D 57, 6003 (1998).
M. Gell-Mann J. B. Hartle (1993) Phys. Rev D 47 3345 Occurrence Handle1993PhRvD..47.3345G Occurrence Handle94d:81013
R. B. Griffths, J. Stat. Phys. 36, 219 (1984); R. Omnés, J. Stat Phys. 53, 893, 933, 957 (1988); Ann. Phys. (NY) 201, 354 (1990); Rev. Mod. Phys. 64, 339 (1992); The Interpretation of Quantum Mechanics (Princeton University Press, 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); 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).
P. W. Milonni, The Quantum Vacuum (Academic, San Diego, 1994); F. Rohrlich, Classical Charged Particles (Addison-Wesley, Reading, MA, 1965).
M. Abraham and R. Becker, Electricity and Magnetism (Blackie, London, 1937); H. A. Lorentz, The Theory of Electrons (Dover, New York, 1952), pp. 49 and 253; P. A. M. Dirac, Proc. R. Soc. Lond. A 167, 148 (1938).
N. V. Kampen, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 26 (1951); E. Moniz and D. Sharp, Phys. Rev. D 10, 1133 (1974); H. Levine, E. Moniz, and D. Sharp, Am. J. Phys. 45, 75 (1977); J. Wheeler and R. Feynman, Rev. Mod. Phys. 17, 157 (1945); F. E. Low, Ann. Phys. 266, 274 (1998); V. Krivitskii and V. Tsytovich, Sov. Phys. Usp. 34, 250 (1991).
H. Callen and T. Welton, Phys. Rev. 83, 34 (1951); H. Mori, Prog. Theor. Phys. 33, 423 (1965); G. W. Ford, M. Kac, and P. Masur, J. Math. Phys. 6, 504 (1965); H. Haken, Rev. Mod. Phys. 80, 67 (1975); H. Dekker, Phys. Rep. 80, 1 (1981).
G. W. Ford, J. T. Lewis, and R. F. O’Connell, Phys. Rev. Lett. 55, 2273 (1985); Phys. Rev. A 37, 4419 (1988); G. W. Ford and R. F. O’Connell, Phys. Lett. A 157, 217 (1991); Phys. Lett. A 174, 182 (1993); G. W. Ford and R. F. O’Connell, Phys. Rev. A 57, 3112 (1998).
L. Diósi, Found. Phys. 20, 63 (1990); P.M.V.B. Barone and A.O. Caldeira, Phys. Rev. A 43, 57 (1991); L. H. Ford, Phys. Rev. D 47, 5571 (1993); Phys. Rev. A 56, 1812 (1997); H-P. Breuer and F. Petruccione, in Relativistic Quantum Measurement and Decohernce, H-P. Breuer and F. Petruccione, eds. (Springer-Verlag, Berlin, Germany, 2000).
For reviews see, e.g., B. L. Hu and E. Verdaguer, Stochastic gravity: A primer with applications, Class. Quant. Grav. 20 (2003) R1-R42 [gr-qc/0211090]; Stochastic gravity: theory and applications, in Living Reviews in Relativity 7 (2004) 3; article number lrr-2004-3 [grqc/ 0307032].
B. L. Hu, P. R. Johnson, and A. Roura, Some conceptual issues in self-consistent backreaction problems, (in preparation).
S. W. Hawking, Nature 248, 30 (1974); Com. Math. Phys. 43, 199 (1975).
A. Raval B. L. Hu J. Anglin (1996) Phys. Rev D 53 7003 Occurrence Handle1996PhRvD..53.7003R
B. L. Hu A. Raval (2001) Is there radiation in Unruh effect? Pisin Chen (Eds) Quantum Aspects of Beam Physics World Scientific Singapore
A. Raval B. L. Hu D. Koks (1997) Phys Rev. D 55 4795 Occurrence Handle1997PhRvD..55.4795R
B. L. Hu P. R. Johnson (2001) Beyond Unruh effect: nonequilibrium quantum dynamics of moving charges Pisin Chen (Eds) Quantum Aspects of Beam Physics World Scientific Singapore
P. Chen T. Tajima (1999) Phys. Rev. Lett. 83 256 Occurrence Handle1999PhRvL..83..256C
W. G. Unruh (1992) Phys Rev. D 46 3271 Occurrence Handle1992PhRvD..46.3271U Occurrence Handle93g:83057
S. Massar R. Parentani (1996) ArticleTitleFrom vacuum fluctuations to radiation. I. Accelerated detectors Phys. Rev. D 54 7426–7443 Occurrence Handle1996PhRvD..54.7426M
Cl. Gabriel Ph. Spindel S. Massar R. Parentani (1998) ArticleTitleInteracting charged particles in an electric field and the Unruh effect Phys. Rev. D 57 6496–6510 Occurrence Handle1998PhRvD..57.6496G
L.D. Romero J.P. Paz (1997) Phys. Rev. A 55 4070 Occurrence Handle1997PhRvA..55.4070D
S-Y. Lin pointed out (private communication) that the factors involving żμφext were missing in Ref 10. These factors didn’t play a role in the specific application treated in Ref. 10, but are necessary for the full consistency of the equations of motion. We thank him for this observation.
L.D. Landau E.M. Liftshitz (1975) Classical Theory of Fields Pergamon New York
J.M. Aguirregabiria (1997) J. Phys. A. Math. Gen. 30 2391 Occurrence Handle10.1088/0305-4470/30/7/019 Occurrence Handle1997JPhA...30.2391A Occurrence Handle0934.34002 Occurrence Handle98d:81007
L. P. Horwitz, (private communication).
J.P. Paz S. Sinha (1992) Phys. Rev. 45 2823 Occurrence Handle1992PhRvD..45.2823P Occurrence Handle93b:83025
B. L. Hu, General relativity as geometro-hydrodynamics, Invited talk at the Second Sakharov Conference, Moscow, May, 1996 [gr-qc/9607070].
C. Anastopoulos (2001) ArticleTitleQuantum correlation functions and the classical limit Phys. Rev. 63 125024 Occurrence Handle2001PhRvD..63L5024A Occurrence Handle2002e:81113
E. Calzetta A. Roura E. Verdaguer (2003) ArticleTitleStochastic description of quantum open systems Physica. 319 188–212 Occurrence Handle2004b:82038
J.R. Anglin (1993) Phys. Rev. D 47 4525 Occurrence Handle1993PhRvD..47.4525A
Fred Cooper Salman Habib Yuval Kluger Emil Mottola Juan Pablo Paz (1994) Phys Rev. 50 2848–2869 Occurrence Handle1994PhRvD..50.2848C
Ya. Zel’dovich and A. Starobinsky, Zh. Eksp. Teor. Fiz 61, 2161 (1971) [Sov. Phys.- JETP 34, 1159 (1971)]; B. L. Hu and L. Parker, Phys. Rev. D 17, 933 (1978); F. V. Fischetti, J. B. Hartle and B. L. Hu, Phys. Rev. D 20, 1757 (1979); J. B. Hartle and B. L. Hu, Phys. Rev. D 20, 1772 (1979); P. A. Anderson, Phys. Rev. D 28, 271 (1983); 29, 615 (1984); E. Calzetta and B. L. Hu,Phys. Rev. D 35, 495 (1987); A. Campos and E. Verdaguer, Phys. Rev. D 49, 1861 (1994).
E. Calzetta and B. L. Hu, Correlations, decoherence, disspation and noise in Quantum Field Theory, in Heat Kernel Techniques and Quantum Gravity, S. Fulling, ed. (Texas A & M Press, College Station, 1995) [hep-th/9501040]; E. Calzetta and B. L. Hu, Phys. Rev. D 61, 025012 (2000).
A. Roura and E. Verdaguer, in preparation (2005).
C. Schubert, Perturbative quantum field theory in the String-inspired formalism Phy. Rep. 355 (2001) 73-234; Z. Bern and D. A. Kosower, Phys. Rev. Lett. 66, 1669 (1991).
M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory (Cambridge University, Cambridge, 1990); E. Witten, Phys. Today 49, 24 (1996); J. Polchinsky, Superstring Theory (Cambridge University Press, Cambridge, 1998).
B. L. Hu (2002) ArticleTitleA kinetic theory approach to quantum gravity Intl J Theor Phys. 41 2111–2138
Pisin Chen (2001) Quantum Aspects of Beam Physics World-Scientific Singapore
F. Bastianelli A. Zirotti (2002) Nucl. Phys. B 642 372 Occurrence Handle2002NuPhB.642..372B Occurrence Handle2003g:81153
Chad Galley and B. L. Hu, Stochastic self-force from radiation reaction in curved spacetime, (in preparation).
Chad Galley, B. L. Hu, and S.Y. Lin, Electromagnetic and gravitational radiation reaction equations from stochastic field theory, in preparation.
P. M. Alsing G. J. Milburn (2003) ArticleTitleTeleportation with a uniformly accelerated partner Phys. Rev. Lett. 91 180404 Occurrence Handle10.1103/PhysRevLett.91.180404 Occurrence Handle2003PhRvL..91r0404A
T. Yu J.H. Eberly (2004) ArticleTitle"Finite-time disentanglement via spontaneous emission Phys. Rev. Lett. 93 140404 Occurrence Handle2004PhRvL..93n0404Y
S. Shresta, C. Anastopoulos, A. Dragulescu, and B. L. Hu, Non-Markovian qubit dynamics in a thermal field bath: relaxation, decoherence and entanglement, Phys. Rev. A [quantph/ 0408084].
C. H. Chou and B. L. Hu, Two qubits disentanglement in an effective spin-boson model, in preparation.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Johnson, P.R., Hu, B.L. Uniformly Accelerated Charge in a Quantum Field: From Radiation Reaction to Unruh Effect. Found Phys 35, 1117–1147 (2005). https://doi.org/10.1007/s10701-005-6404-1
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10701-005-6404-1