Unified treatment of some Casimir energies and Lamb shifts: A dielectric between two ideal conductors

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 57, Issue 2, 1998, Pages 1108-1120

  Schaden, Martin ^a   Spruch, Larry ^a,b,c   Zhou, Fei ^a,d  

^a POLYTECHNIC UNIVERSITY   (United States)

^b MAX PLANCK INSTITUT FÜR KERNPHYSIK   (Germany)

^c UNIVERSITY OF HEIDELBERG   (Germany)

^d LEHMAN BROTHERS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIELECTRIC PROPERTIES; ELECTRIC CONDUCTORS; ELECTRIC FIELD EFFECTS; ELECTRON ENERGY LEVELS; ELECTRONIC DENSITY OF STATES; PERMITTIVITY; PROBABILITY DENSITY FUNCTION; RADIATION EFFECTS;

CASIMIR ENERGIES; KRAMERS-KRONIG RELATION; LAMB SHIFTS; QUANTUM ELECTRODYNAMICS;

QUANTUM THEORY;

EID: 0032002860     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.57.1108     Document Type: Article

References (35)

1. See, for example, S. Hawking, Commun. Math. Phys. 55, 133 (1977); CMPHAYW. Dittrich and M. Reuter, Effective Lagrangians in Quantum Electrodynamics, Lecture Notes in Physics Vo1. 220 (Springer, Berlin, 1985), for a vacuum between the plates, andM. Schaden and L. Spruch (unpublished), for a dielectric between the plates.
2. H. A. Bethe, Phys. Rev. 72, 241 (1947); PHRVAOsee also S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Harper & Row, New York, 1962), p. 524ff.
3. H. B. G. Casimir, J. Chim. Phys. Phys.-Chim. Biol. 46, 407 (1949).JCPBAN
4. G. Barton, Proc. R. Soc. London, Ser. A 410, 141 (1987).PRLAAZ
5. E. J. W. Verwey and J. T. G. Overbeek, Theory of the Stability of Lyophobic Colloids (Elsevier, Amsterdam, 1948).
6. H. B. G. Casimir and D. Polder, Phys. Rev. 73, 360 (1948).PHRVAO
7. H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 60, 793 (1948).PKNAAU
8. E. M. Lifshitz, Zh. Éksp. Teor. Fiz. 29, 94 (1955) [Sov. Phys. JETP 2, 73 (1956)]; SPHJAR[see also L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, Course of Theoretical Physics Vol. 2, 4th revised English ed. (Pergamon, New York, 1975)];
9. I. E. Dzyaloshinskii, E. M. Lifshitz, and L. Pitaevskii, Adv. Phys. 10, 165 (1961).ADPHAH
10. B. V. Derjaguin and I. I. Abriksova, Zh. Éksp. Teor. Fiz. 30, 993 (1956) [Sov. Phys. JETP 3, 819 (1957)]; SPHJAR
11. M. J. Sparnaay, Physica (Amsterdam) 24, 751 (1958); PHYSAG
12. J. N. Israelachvili and D. Tabor, Proc. R. Soc. London, Ser. A 331, 19 (1972).PRLAAZ
13. P. W. Milonni, The Quantum Vacuum (Academic, New York, 1993). See especially Chaps. 7 and 8.
14. E. Hinds, in Cavity Quantum Electrodynamics, supplement to Advances in Atomic, Molecular, and Optical Physics, edited by P. R. Berman (Academic Press, New York, 1994), Chap. 1.
15. L. Spruch, in Long-Range Casimir Forces: Theory and Experiment in Multiparticle Dynamics, edited by F. S. Levin and D. A. Micha (Plenum, New York, 1993), Chap. 1.
16. Y. Tikochinsky and L. Spruch, Phys. Rev. A 48, 4223 (1993).PLRAAN
17. F. Zhou and L. Spruch, Phys. Rev. A 52, 297 (1995).PLRAAN
18. S. Lamoreaux, Phys. Rev. Lett. 78, 5 (1997).PRLTAO
19. N. G. van Kampen, B. R. A. Nijboer, and K. Schramm, Phys. Lett. 26A, 307 (1968).PYLAAG
20. See, for example, E. A. Power, Introductory Quantum Electrodynamics (Elsevier, Amsterdam, 1964), p. 131, or
21. R. W. Robinett, Quantum Mechanics (Oxford, New York, 1997), p. 481.
22. For (Formula presented) and a vacuum between the plates, that is (Formula presented), we have (Formula presented), where (Formula presented) is the angle of incidence of the mode under consideration on one of the walls.
23. Consider, for instance, the simple case for which the region between the plates is the physical vacuum [not the ideal vacuum with (Formula presented) everywhere]. For any value of (Formula presented) of physical interest one can set (Formula presented), but for (Formula presented) of the order of a Compton wavelength, vacuum polarization is affected by the presence of the walls and (Formula presented) for all but very high frequencies is independent of (Formula presented) but dependent upon (Formula presented). See G. Barton and K. Scharnhorst, J. Phys. A 26, 2037 (1993).JPHAC5
24. See, for example, E. Merzbacher, Quantum Mechanics, 2nd ed. (Wiley, New York, 1970), p. 458.
25. The mass in Eq. (3.28) is the electron’s observed physical mass (Formula presented), since this relation is derived for (renormalized) physical quantities, analogous to the fact that the similarly derived relation between plasma frequency and electron density in Eq. (3.24) also involves only the observed electron mass.
26. R. P. Feynman, in The Present Status of Quantum Electrodynamics, edited by R. Stoops (Wiley Interscience, New York, 1961).
27. See also E. A. Power, Am. J. Phys. 34, 516 (1966), AJPIASand Ref. 10, p. 92.
28. G. Barton, Proc. R. Soc. London, Ser. A 320, 251 (1970).PRLAAZ
29. L. Spruch and Y. Tikochinsky, Phys. Rev. A 48, 4213 (1993).PLRAAN
30. R. J. Glauber and M. Lewenstein, Phys. Rev. A 43, 467 (1991).PLRAAN
31. M. Matloob, R. Loudon, S. M. Barnett, and J. Jeffers, Phys. Rev. A 52, 4823 (1995); PLRAAN
32. Phys. Rev. AM. Matloob and R. Loudon, 53, 4567 (1996).
33. D. Kupiszewska and J. Mostowski, Phys. Rev. A 41, 4636 (1990).PLRAAN
34. G. Barton, Proc. R. Soc. London, Ser. A (to be published).
35. P. W. Milonni, J. Mod. Opt. 42, 1191 (1995). JMOPEW