D. Robaschik, K. Scharnhorst, E. Wieczorek: Radiative corrections to the Casimir pressure under the influence of temperature and external fields. Annals of Physics (New York) 174:2(1987)401-429 (DOI: 10.1016/0003-4916(87)90034-0). [INSPIRE record]

Abstract: Generalizing the quantum field theory (QFT) with boundary conditions in covariant gauge to the case of finite temperature, we develop the quantum electrodynamics (QED) with boundary conditions in the Matsubara approach as well as in the thermofield formulation. We rederive the known results of the free-field theory for the pressure and the free energy of the Casimir problem. For infinitely thin plates we calculate the radiative corrections in second-order perturbation theory at finite temperature. Thereby it turns out that the calculation of the vacuum energy at the vanishing temperature via the Z functional is much simpler than a calculation via the energy momentum tensor. This observation allows determination of the influence of static electromagnetic fields on the Casimir problem.

• Electronic copy of the article: Annals of Physics (New York)
• Citations

• Misprints, errata, addenda (PDF / Postscript):
  • P. 419, eq. (4.40), the sign of the r.h.s. should be reversed, cf.:
    • footnote 1 on p. 357 of: K. Scharnhorst: On propagation of light in the vacuum between plates. Physics Letters B 236(1990)354-359 (DOI: 10.1016/0370-2693(90)90997-K). = paper [16],
      
    • also, H. Gies: QED effective action at finite temperature: Two loop dominance Physical Review D 61(2000)085021, 18 pp. [hep-ph/9909500] (DOI: 10.1103/PhysRevD.61.085021), (in particular footnote 8 on p. 085021-14).
      
    The discussion of the imaginary part on p. 419 has to be adjusted correspondingly.
  • P. 424, eq. (II.8), the sign after F₀ should be reversed (from minus to plus).
  • P. 429, eq. (II.9), the sign after F₀ should be reversed (from minus to plus), and for a correction of a misprint in the photon propagator see this sheet: PDF / Postscript.
  • P. 425, eq. (II.11), second line, the sign after F₀(a,β) should be reversed (from minus to plus).

© K. Scharnhorst . Document last modified: June 8, 2023