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Field Fluctuations and Casimir Energy of 1D-Fermions

Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, 47011 Valladolid, Spain
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Symmetry 2019, 11(5), 643; https://doi.org/10.3390/sym11050643
Received: 15 April 2019 / Revised: 2 May 2019 / Accepted: 4 May 2019 / Published: 7 May 2019
(This article belongs to the Special Issue Symmetry Breaking in Quantum Phenomena)
We investigate the self-adjoint extensions of the Dirac operator of a massive one-dimensional field of mass m confined in a finite filament of length L. We compute the spectrum of vacuum fluctuations of the Dirac field under the most general dispersionless boundary conditions. We identify its edge states in the mass gap within a set of values of the boundary parameters, and compute the Casimir energy of the discrete normal modes. Two limit cases are considered, namely, that of light fermions with m L 1 , and that of heavy fermions for which m L 1 . It is found that both positive and negative energies are obtained for different sets of values of the boundary parameters. As a consequence of our calculation we demonstrate that the sign of the quantum vacuum energy is not fixed for exchange-symmetric plates (parity-invariant configurations), unlike for electromagnetic and scalar fields. View Full-Text
Keywords: vacuum fluctuations; boundary conditions; Dirac field; Casimir effect vacuum fluctuations; boundary conditions; Dirac field; Casimir effect
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MDPI and ACS Style

Donaire, M.; Muñoz-Castañeda, J.M.; Nieto, L.M.; Tello-Fraile, M. Field Fluctuations and Casimir Energy of 1D-Fermions. Symmetry 2019, 11, 643. https://doi.org/10.3390/sym11050643

AMA Style

Donaire M, Muñoz-Castañeda JM, Nieto LM, Tello-Fraile M. Field Fluctuations and Casimir Energy of 1D-Fermions. Symmetry. 2019; 11(5):643. https://doi.org/10.3390/sym11050643

Chicago/Turabian Style

Donaire, Manuel, José M. Muñoz-Castañeda, Luis M. Nieto, and Marcos Tello-Fraile. 2019. "Field Fluctuations and Casimir Energy of 1D-Fermions" Symmetry 11, no. 5: 643. https://doi.org/10.3390/sym11050643

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