Prog. Theor. Phys. Supplement No.88 (1986) pp. 1-142

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Vacuum Noise and Stress Induced by Uniform Acceleration

— Hawking-Unruh Effect in Rindler Manifold of Arbitrary Dimension —

Department of Physics, Tohoku University, Sendai 980
and
Department of Astrophysics, University of Oxford, South Parks Road, Oxford, OX1 3RQ, England

(Received September 22, 1986)

Abstract:

This is a comprehensive account of a particular recent development concerning the thermal character inherent in the quantum field as viewed from a uniformly accelerated frame of reference. That is, the power spectrum of the vacuum noise (or the detector-response function) seen by a uniformly accelerated obsever in flat specetimes of arbitrary dimensions is investigated and is shown to exhibit the phenomenon of the apparent inversion of statistics in odd dimensions. Its relation to the thermalization theorem is clarified. Also discussed are the closely related phenomena occurring in the vacuum stress of the Rindler manifold and in the noise seen by a comoving observer in the de Sitter spacetime, as well as those associated with the circular motion in the flat spacetime.

URL : http://ptp.ipap.jp/link?PTPS/88/1/
DOI : 10.1143/PTPS.88.1

References:

G. Barton and N. Dombay, Ann. of Phys. 162 (1985), 231[Elsevier].
J. D. Bekenstein, Phys. Rev. D 7 (1973), 2333[APS].
J. S. Bell and J. M. Leinaas, Nucl. Phys. B 212 (1983), 131[CrossRef].
J. S. Bell and J. M. Leinaas, “The Unruh Effect and Quantum Fluctuation of Electrons in Storage Rings”, Preprint (1986).
J. S. Bell, R. J. Hughes and J. M. Leinaas, Z. Phys. C 28 (1985), 75.
N. D. Birrell and P. C. W. Davies, Phys. Rev. D 18 (1978), 4408[APS].
N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, 1982).
J. J. Bisognano and E. H. Wichmann, J. Math. Phys. 16 (1975), 985[AIP Scitation].
J. J. Bisognano and E. H. Wichmann, J. Math. Phys. 17 (1976), 303[AIP Scitation].
J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, 1965).
N. J. Bogoliubov, Phys. USSR 11 (1947), 23.
D. G. Boulware, Phys. Rev. D 11 (1975a), 1404[APS].
D. G. Boulware, Phys. Rev. D 12 (1975b), 350[APS].
T. H. Boyer, Phys. Rev. D 21 (1980), 2137[APS].
T. H. Boyer, Phys. Rev. D 29 (1984a), 1096[APS].
T. H. Boyer, Phys. Rev. D 30 (1984b), 1228[APS].
M. R. Brown, A. Ottewill and S. T. C. Siklos, Phys. Rev. D 26 (1982), 1881[APS].
M. R. Brown and A. C. Ottewill, Proc. R. Soc. London A 389 (1983) 379.
P. Candelas, Phys. Rev. D 21 (1980), 2185[APS].
P. Candelas, P. Chrzanowski and K. W. Howard, Phys. Rev. D 24 (1981), 297[APS].
P. Candelas and D. Deutsch, Proc. R. Soc. London A 354 (1977), 79.
P. Candelas and D. Deutsch, Proc. R. Soc. London A 362 (1978), 251.
P. Candelas and J. S. Dowker, Phys. Rev. D 19 (1979), 2902[APS].
P. Candelas and D. J. Raine, J. Math. Phys. 17 (1976), 2101[AIP Scitation].
P. Candelas and D. W. Sciama, Phys. Rev. Lett. 38 (1977), 1372[APS].
S. M. Christensen and M. J. Duff, Nucl. Phys. B 146 (1978), 11[CrossRef].
S. M. Christensen and S. A. Fulling, Phys. Rev. D 15 (1977), 2088[APS].
D. C. Cole, Phys. Rev. D 31 (1985), 1972[APS].
E. J. Copeland, P. C. W. Davies and K. Hinton, Class. Quantum Grav. 1 (1984), 179[IoP STACKS].
R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience Publishers, 1962), vol. II.
P. C. W. Davies, J. of Phys. A 8 (1975), 609[IoP STACKS].
P. C. W. Davies, Rep. Prog. Phys. 41 (1978), 1313[IoP STACKS].
P. C. W. Davies, in Quantum Theory of Gravity, ed. S. M. Christensen (Adam Hilger, 1984), p. 66.
P. C. W. Davies and D. J. Toms, Phys. Rev. D 31 (1985), 1363[APS].
P. D. D'Eath and J. J. Halliwell, “Fermions in Quantum Cosmology”, Preprint. (1986)
B. S. DeWitt, Phys. Rep. 19 (1975), 295[CrossRef].
B. S. DeWitt, in General Relativity, ed. S. W. Hawking and W. Israel (Cambridge University Press, 1979), p. 680.
J. S. Dowker, J. of Phys. A 10 (1977), 115[IoP STACKS].
J. S. Dowker, Phys. Rev. D 18 (1978), 1856[APS].
A. Einstein, B. Podolsky and N. Rosen, Phys. Rev. 47 (1935), 777[APS].
A. Einstein and N. Rosen, Phys. Rev. 48 (1935), 73[APS].
A. Eldélyi, W. Magnas, F. Oberhettinger and F. G. Tricomi, Tables of Integral Transforms (McGraw-Hill, 1954), vol. II, p. 145.
R. Figari, R. Hoegh-Krohn and C. Nappi, Commun. Math. Phys. 44 (1975), 265[CrossRef].
L. H. Ford, Phys. Rev. D 12 (1977), 2963[APS].
K. Freeze, C. T. Hill and M. Mueller, Nucl. Phys. B 255 (1985), 693[CrossRef].
R. Friedberg, T. D. Lee and Y. Pang, Nucl. Phys. B 276 (1986), 549[Elsevier].
V. P. Frolov and V. L. Ginzburg, Phys. Lett. A 116 (1986), 423[Elsevier].
S. A. Fulling, Phys. Rev. D 7 (1973), 2850[APS].
S. A. Fulling, J. of Phys. A 10 (1977), 917[IoP STACKS].
S. A. Fulling, Gen. Relat. Gravit. 10 (1979), 807.
S. A. Fulling and S. N. M. Ruijsenaas, “Temperature, Periodicity and Horizons”, Preprint. (1985)
H. Georgi, Lie Algebras in Particle Physics (Benjamin/Cummings, 1982).
U. H. Gerlach, Phys. Rev. D 27 (1983a), 2310[APS].
U. H. Gerlach, Phys. Rev. D 28 (1983b), 761[APS].
U. H. Gerlach, Found. Phys. 16 (1986), 667.
G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15 (1977a), 2738[APS].
G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15 (1977b), 2752[APS].
G. W. Gibbons and M. J. Perry, Phys. Rev. Lett. 36 (1976), 985[APS].
G. W. Gibbons and M. J. Perry, Proc. R. Soc. London A 358 (1978), 467.
G. W. Gibbons and D. L. Wiltshire, Ann. of Phys. 167 (1986), 201[CrossRef].
P. G. Grove, Class. Quantum Grav. 3 (1986a), 793[IoP STACKS].
P. G. Grove, Class. Quantum Grav. 3 (1986b), 801[IoP STACKS].
P. G. Grove and A. C. Ottewill, J. of Phys. A 16 (1983), 3905[IoP STACKS].
P. G. Grove and A. C. Ottewill, Class. Quantum Grav. 2 (1985), 373[IoP STACKS].
R. Haag, H. Narnhofer and U. Stein, Commun. Math. Phys. 94 (1984), 219.
S. Hacyan, Phys. Rev. D 32 (1985), 3216[APS].
P. Hájicék, Phys. Rev. D 15 (1977), 2757[APS].
P. R. Halmos, Measure Theory (Springer Verlag, 1974).
J. B. Hartle and S. W. Hawking, Phys. Rev. D 13 (1976), 2188[APS].
S. W. Hawking, Nature 248 (1974), 30[CrossRef].
S. W. Hawking, Commun. Math. Phys. 43 (1975), 199[CrossRef].
S. W. Hawking, Phys. Rev. D 13 (1976), 191[APS].
C. T. Hill, Phys. Lett. B 155 (1985), 343[Elsevier].
C. T. Hill, Nucl. Phys. B 277 (1986), 547[Elsevier].
K. J. Hinton, J. of Phys. A 16 (1983), 1937[IoP STACKS].
K. J. Hinton, Class. Quantum Grav. 1 (1984), 27[IoP STACKS].
K. Hinton, P. C. W. Davies and J. Pfautsch, Phys. Lett. B 120 (1983), 88[Elsevier].
M. Horibe, Prog. Theor. Phys. 61 (1979), 661[IPAP].
M. Horibe, A. Hosoya and N. Yamamoto, Prog. Theor. Phys. 74 (1985), 1299[IPAP].
W. Israel, Phys. Lett. A 57 (1976), 107[CrossRef].
W. Israel, and J. M. Nester, Phys. Lett. A 98 (1983), 329[Elsevier].
C. Itzykson and J. B. Zuber, Quantum Field Theory (McGraw-Hill, 1980).
B. R. Iyer, Phys. Rev. D 26 (1982), 1900[APS].
B. R. Iyer, and A. Kumar, Pramãna 9 (1977), 441.
B. R. Iyer, and A. Kumar, J. of Phys. A 13 (1980), 469[IoP STACKS].
B. S. Kay, Commun. Math. Phys. 100 (1985a), 57.
B. S. Kay, Helv. Phys. Acta 58 (1985b), 1017; ibid. 58 (1985b), 1030.
R. Kubo, J. Phys. Soc. Jpn. 12 (1957), 570[IPAP].
T. D. Lee, Nucl. Phys. B 264 (1986a), 437[CrossRef].
T. D. Lee, Prog. Theor. Phys. Suppl. No. 85 (1986b), 271[IPAP].
A. J. Leggett, Prog. Theor. Phys. Suppl. No. 69 (1980), 80[IPAP].
J. R. Letaw, Phys. Rev. D 23 (1981), 1709[APS].
J. R. Letaw and J. D. Pfautsch, Phys. Rev. D 22 (1980), 1345[APS].
J. R. Letaw and J. D. Pfautsch, Phys. Rev. D 24 (1981), 1491[APS].
P. C. Martin and J. Schwinger, Phys. Rev. 115 (1959), 1342[APS].
P. Meyer, Phys. Rev. D 18 (1978), 609[APS].
C. W.Misner, K. S. Thorne and J. A. Wheeler, Gravitation (W. H. Freeman and Company, 1973).
N. P. Myhrvold, Phys. Lett. A 100 (1984), 345[Elsevier].
N. P. Myhrvold, Ann. of Phys. 160 (1985), 102[Elsevier].
H. Ooguri, Phys. Rev. D 33 (1985), 3573[APS].
A. C. Ottewill and S. Takagi, Prog. Theor. Phys. 77 (1987), 310[IPAP].
T. Padmanabhan, Class. Quantum Grav. 2 (1985), 117[IoP STACKS].
L. Parker, Phys. Rev. D 12 (1975), 1519[APS].
R. Peierls, Surprises in Theoretical Physics (Princeton University Press, 1979).
R. Penrose and W. Rindler, Spinors and Space-Time (Cambridge University Press 1986), vol. 2.
D. Pines and P. Nozières, The Theory of Quantum Liquids (Benjamin, 1966).
B. Ratra, Phys. Rev. D 31 (1985), 1931[APS].
I. H. Redmount and S. Takagi, “Hyperspherical Rindler Space, Dimensional Reduction, and de Sitter-space Scalar Field Theory”, Preprint. (1986)
W. Rindler, Am. J. Phys. 34 (1966), 1174.
H. Rumpf, Phys. Rev. D 28 (1983), 2946[APS].
N. Sakai, in Essays in Honor of the 60th Birthday of Professor Yoshio Yamaguchi (World Scientific Pub., 1986), to appear.
N. Sánchez, Phys. Lett. B 87 (1979), 212[Elsevier].
N. Sánchez, Phys. Lett. B 105 (1981a), 375[Elsevier].
N. Sánchez, Phys. Lett. A 81 (1981b), 424[Elsevier].
N. Sánchez, Phys. Rev. D 24 (1981c), 2100[APS].
N. Sánchez, Phys. Lett. A 112 (1985), 133[Elsevier].
N. Sánchez and B. F. Whiting, Phys. Rev. D 34 (1986), 1056[APS].
G. L. Sewell, Phys. Lett. A 79 (1980), 23[Elsevier].
G. L. Sewell, Ann. of Phys. 141 (1982), 201[CrossRef].
D. W. Sciama, in Relativity, Quanta and Cosmology, ed. M. Pantaleo and F. De Finis (Johnson Reprint Corporation, 1979), vol. II.
D. W. Sciama, P. Candelas and D. Deutsch, Adv. Phys. 30 (1981), 327.
M. Soffel, B. Müller and W. Greiner, Phys. Rev. D 22 (1980), 1935[APS].
S. Takagi, Prog. Theor. Phys. 72 (1984a), 505[IPAP]; ibid. 72 (1984a), 1270[IPAP].
S. Takagi, Phys. Lett. B 148 (1984b), 116[Elsevier].
S. Takagi, Prog. Theor. Phys. 74 (1985), 142[IPAP]; ibid. 74 (1985), 501[IPAP]; ibid. 74 (1985), 1219[IPAP].
Y. Takahashi and H. Umezawa, Collective Phenomena 2 (1975), 55.
W. Thirring, Found. Phys. 13 (1983), 409.
R. C. Tolman, Relativity, Thermodynamics and Cosmology (Clarendon Press, 1934).
A. Tomimatsu, Prog. Theor. Phys. 74 (1985), 630[IPAP].
W. Troost and H. Van Dam, Phys. Lett. B 71,(1977), 149[Elsevier].
W. Troost and H. Van Dam, Nucl. Phys. B 152 (1979), 442[CrossRef].
H. Umezawa, H. Matsumoto and M. Tachiki, Thermo Field Dynamics and Condensed States (North Holland, 1982).
W. G. Unruh, Phys. Rev. D 14 (1976), 870[APS].
W. G. Unruh, Can. J. Phys. 64 (1986a), 128.
W. G. Unruh, Phys. Rev. D 34 (1986b), 1222[APS].
W. G. Unruh and R. M. Wald Phys. Rev. D 29 (1984), 1047[APS].
W. G. Unruh and N. Weiss, Phys. Rev. D 29 (1984), 1656[APS].
R. M. Wald, Commun. Math. Phys. 45 (1975), 9[CrossRef].
R. M. Wald, General Relativity (The University of Chicago Press, 1984), chap. 14.
S. Weinberg, Gravitation and Cosmology (Wiley, 1972).
E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed. (Cambridge University Press, 1965).
M. Yoshimura, Phys. Rev. D 34 (1986), 1021[APS].
Ya. B. Zel'dovich, L. V. Rozhanskii and A. A. Starobinskii, JETP Lett. 43 (1986), 523.

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