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Schwinger's method for the fermionic Casimir effect

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Abstract

The Casimir energy of a massive Dirac field confined between two parallel infinite plates is computed using a method proposed by Schwinger. The massless case is obtained as a limit of the massive case. The boundary conditions are those of zero current through the plates, as inspired by quark confinement in the MIT bag model for hadrons. We use an analytical continuation method of regularization which allows the employment of Epstein function techniques. The calculation using Schwinger's original regularization by a cutoff in proper time is also outlined.

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Cougo-Pinto, M.V., Farina, C. & Tort, A. Schwinger's method for the fermionic Casimir effect. Lett Math Phys 38, 97–101 (1996). https://doi.org/10.1007/BF00398302

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Mathematics Subject Classifications (1991)

  • 81V10
  • 33D10

Key words

  • Casimir effect
  • Dirac fields
  • MIT bag model
  • Casimir energy