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Peer-reviewedCC BY-NC-ND 4.0Complex Analysis and Operator Theory

The Pauli-Villars-Regularised Dirac Field Coupled to Electromagnetic Fields at Thermal Equilibrium

  • William Borrelli
  • Umberto Morellini
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Abstract

In this paper we consider a model for the Dirac field in a classical electromagnetic field at thermal equilibrium. We adopt the Pauli-Villars regularisation technique in order to properly define the free energy of the equilibrium state, extending the previous work by the second named author on the purely magnetic case. This work provides a first step towards understanding polarisation effects in the Dirac field at thermal equilibrium, in the presence of both electrostatic and magnetic potentials.

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Cite

BibTeXRIS
BibTeX
@article{borrelli2026paulivillarsregularised,
  title = {{The Pauli-Villars-Regularised Dirac Field Coupled to Electromagnetic Fields at Thermal Equilibrium}},
  author = {William Borrelli and Umberto Morellini},
  journal = {Complex Analysis and Operator Theory},
  year = {2026},
  month = sep,
  doi = {10.1007/s11785-026-02049-6},
  eprint = {2601.16743},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05771774v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - JOUR
TI  - The Pauli-Villars-Regularised Dirac Field Coupled to Electromagnetic Fields at Thermal Equilibrium
AU  - William Borrelli
AU  - Umberto Morellini
PY  - 2026
DA  - 2026/09/30
JO  - Complex Analysis and Operator Theory
DO  - 10.1007/s11785-026-02049-6
UR  - https://hal.science/hal-05771774v1
AB  - In this paper we consider a model for the Dirac field in a classical electromagnetic field at thermal equilibrium. We adopt the Pauli-Villars regularisation technique in order to properly define the free energy of the equilibrium state, extending the previous work by the second named author on the purely magnetic case. This work provides a first step towards understanding polarisation effects in the Dirac field at thermal equilibrium, in the presence of both electrostatic and magnetic potentials.
SN  - 1661-8254
SN  - 1661-8262
ER  -