quantum algorithms:
spin geometry, string geometry, fivebrane geometry …
rotation groups in low dimensions:
see also
The differential equation encoded by a Dirac operator.
The equations of motion of the Dirac field.
Monographs on the relativistic Dirac equation in 3+1d Minkowski spacetime:
James D. Bjorken, Sidney D. Drell: Relativistic Quantum Mechanics, McGrawHill (1964) [ark:/13960/t5fc2v05h, pdf, pdf]
Bernd Thaller, The Dirac Equation, Texts and Monographs in Physics, Springer (1992) (doi:10.1007/978-3-662-02753-0)
See also:
Discussion for curved spacetime:
M. D. Pollock, On the Dirac equation in curved space-time, Acta Physica Polonica B 41 (2010) [InSpire:874211, pdf]
Peter Collas, David Klein: The Dirac equation in general relativity, a guide for calculations, Springer Briefs in Physics, Springer (2019) [arXiv:1809.02764, doi:10.1007/978-3-030-14825-6]
The path integral approach to the Dirac equation:
Takashi Ichinose, Hiroshi Tamura, Path Integral Approach to Relativistic Quantum Mechanics: Two-Dimensional Dirac Equation, Progress of Theoretical Physics Supplement, Volume 92, April 1987, Pages 144–175, doi.
Pierre Gosselin, Janos Polonyi, Path Integral for Relativistic Equations of Motion, arXiv:hep-th/9708121.
Janos Polonyi, Path Integral for the Dirac Equation, arXiv:hep-th/9809115.
Wataru Ichinose, On the Feynman Path Integral for the Dirac Equation in the General Dimensional Spacetime, Communications in Mathematical Physics 329, 83–508 (2014), doi.
Wataru Ichinose, Notes on the Feynman path integral for the Dirac equation, Journal of Pseudo-Differential Operators and Applications 9, 789–809 (2018), doi.
The Dirac equation in a gravitational Schwarzschild spacetime background:
On quantum simulation of the Dirac equation:
L. Lamata, J. León, T. Schätz, Enrique Solano: Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion, Phys. Rev. Lett. 98 253005 (2007) [doi:10.1103/PhysRevLett.98.253005]
R. Gerritsma, G. Kirchmair, F. Zähringer, Enrique Solano, R. Blatt & C. F. Roos: Quantum simulation of the Dirac equation, Nature 463 68–71 (2010) [doi:10.1038/nature08688]
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