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      The Propagator and Path Integral Quantization for the New Dirac Equation

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      New Dirac equation, Dark matter, Path integral, Feynman propagator
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            Revision notes

            Several changes were made in this second revision. The changes are highlighted in orange on the "PDF for tracked changes." The changes include:

             

            Page 5: 

             

            - Equation 25 has been simplified with fewer steps.

            - Equation 29, to be fully consistent with Equation 18, has been corrected by replacing q_a abd q_b with q and the steps shown reflect this. Also, there are fewer steps in equation 29.

             

            Pages 5 and 6:

            - The sentences in the previous version, starting with "Wee see that only the point ..." and "This is also true ..." are not necessary and have been omitted

             

            Page 6:

            - Equation 30 has been corrected by replacing each of the q_1, ... q_n with q as it is not necessary to have distinct q's.

            - In equations 31 and 32, the variables (x, q) have been swapped with the variables (x', q') for consistency of notation with equations 27 and 28.

             

            Page 7:

            - Equation 36 has been simplified with fewer steps.

             

            Page 8:

            - Equation 41, to be fully consistent with Equations 18 and 29, has been corrected by replacing q_a abd q_b with q and the steps shown reflect this. Also, there are fewer steps in equation 41.

            Abstract

            Content

            Author and article information

            Journal
            ScienceOpen Preprints
            ScienceOpen
            26 January 2025
            Affiliations
            [1 ] Unaffiliated, Atlanta, GA, USA;
            Author notes
            Author information
            https://orcid.org/0000-0001-6204-4170
            Article
            10.14293/PR2199.001131.v3
            21b93996-adae-416e-9e31-6758c8bbb884

            This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .

            History
            : 7 October 2024
            Categories

            Data sharing not applicable to this article as no datasets were generated or analysed during the current study.
            Quantum physics & Field theory,High energy & Particle physics,Theoretical physics
            New Dirac equation,Dark matter,Path integral,Feynman propagator

            References

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            2. A positive-energy relativistic wave equation. II. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences. Vol. 328(1572):1–7. 1972. The Royal Society. [Cross Ref]

            3. Dirac P. A. M.. Pretty mathematics. International Journal of Theoretical Physics. Vol. 21(8-9):603–605. 1982. Springer Science and Business Media LLC. [Cross Ref]

            4. Bogomolny Eugene. Positive-Energy Dirac Particles and Dark Matter. Universe. Vol. 10(5)2024. MDPI AG. [Cross Ref]

            5. Klishevich S.M., Plyushchay M.S., Rausch de Traubenberg M.. Fractional helicity, Lorentz symmetry breaking, compactification and anyons. Nuclear Physics B. Vol. 616(3):419–436. 2001. Elsevier BV. [Cross Ref]

            6. Biedenharn L. C., Han M. Y., van Dam H.. Generalization and Interpretation of Dirac's Positive-Energy Relativistic Wave Equation. Physical Review D. Vol. 8(6):1735–1746. 1973. American Physical Society (APS). [Cross Ref]

            7. Manga A. Ousmane, Samsonenko N. V., Moussa A.. Lagrangian formalism for the new Dirac equation. Advanced Studies in Theoretical Physics. Vol. 7:141–150. 2013. Hikari, Ltd. [Cross Ref]

            8. Adamou Ousmane Manga, Aboubacar Moussa, Almoustapha Aboubacar, Vladimirovich Samsonenko Nicolai. Two-component form of the new Dirac equation. Advanced Studies in Theoretical Physics. Vol. 7:319–324. 2013. Hikari, Ltd. [Cross Ref]

            9. Cirilo-Lombardo Diego J., Sanchez Norma G.. Quantum-Spacetime Symmetries: A Principle of Minimum Group Representation. Universe. Vol. 10(1)2024. MDPI AG. [Cross Ref]

            10. CIRILO-LOMBARDO Diego J, SANCHEZ Norma G.. Entanglement and Generalized Berry Geometrical Phases in Quantum Gravity. MDPI AG. [Cross Ref]

            11. Shapiro Ilya L.. Covariant Derivative of Fermions and All That. Universe. Vol. 8(11)2022. MDPI AG. [Cross Ref]

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