Field Fluctuations and Casimir Energy of 1D-Fermions
Abstract
:1. Introduction
2. Fundamentals of the Approach
- Particles moving from left to right with and momentum k, .
- Particles moving from right to left with and momentum k, .
- Anti-particles moving from left to right with and momentum k, .
- Anti-particles moving from right to left with and momentum k, .
3. Spectrum of Fluctuations of the Dirac Field Confined in a Finite Filament
3.1. Construction of the Boundary Spinors and the Boundary Condition
- At the components are determined by the eigenvalue equation . This means that the component of contributes to .
- At the components are determined by the eigenvalue equation . This means that the component of contributes to .
3.2. Normal Modes
3.3. Localised Edge States
4. Casimir Energy of the Dirac Field in 1D
4.1. Casimir Energy of Light Fermions
4.2. Casimir Energy of Heavy Fermions
A Remark on the Sign of the Energy for Heavy Fermions
5. Conclusions and Outlook
Author Contributions
Funding
Conflicts of Interest
References
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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
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 StyleDonaire, Manuel, José María Muñoz-Castañeda, Luis Miguel 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
APA StyleDonaire, M., Muñoz-Castañeda, J. M., Nieto, L. M., & Tello-Fraile, M. (2019). Field Fluctuations and Casimir Energy of 1D-Fermions. Symmetry, 11(5), 643. https://doi.org/10.3390/sym11050643