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      The Propagator and Path Integral Quantization for the New Dirac Equation

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      This is not the latest version for this article. If you want to read the latest version, click here.
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      New Dirac equation, Dark matter, Path integral, Feynman propagator
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            Revision notes

            Several minor changes were made in this revised version. The changes are highlighted in orange on the "PDF for tracked changes." The changes include:

            Page 1: 

            - The beginning of the first paragraph of the manuscript now includes a brief description of the internal structure of the particle

            - Toward the end of the first paragraph of the manuscript, the phrase "for the case of minimal coupling" is inserted.

            Page 2:

            - A comma was inserted at the end of equation 8 and a period at the end of equation 10 for proper punctuation.

            Page 3:

            - A comma was included at the end of equation 14.

            -In the middle of page 3, the subscript "p" was added to the symbols for the fields Psi and \overline{Psi}

            -The operator a_p was inserted into each step of equation 16, and the operator a^{\dagger}_p was inserted into each step of equation 17.

            -The operators a^{\dagger}_p and a_p are described toward the bottom of page 3 in two sentences, the second sentence of which ends on page 4.

            Page 4:

            -The last word and citation at the end of the second sentence describing the previously mentioned operators appear at the top of page 4.

            -Commas were inserted at the ends of equations 18 and 19.

            -The symbols Psi(x) and \overline{Psi}(x) are changed to Psi(x, q) and \overline{Psi}(x, q) toward the end of page 4.

            - A comma was inserted at the end of equation 24.

            Page 6:

            -At the beginning of Section 4, the word "sketch" was changed to the word "treatment."

            -Commas were added at the ends of equations 33 and 34.

            Page 8:

            -A comma was inserted at the end of equation 42.

            Page 9:

            -Commas were added at the ends of equations 45, 46, and 50.

            -A clarification about the coupling constant g was added in parentheses toward the end of page 9.

            Page 10:

            -Commas were inserted at the ends of equations 54 and 55.

            -A period was inserted at the end of equation 56.

            Page 11:

            -A comma was inserted at the end of equation 59.

             

            Abstract

            Content

            Author and article information

            Journal
            ScienceOpen Preprints
            ScienceOpen
            13 October 2024
            Affiliations
            [1 ] Unaffiliated, Atlanta, GA, USA;
            Author notes
            Author information
            https://orcid.org/0000-0001-6204-4170
            Article
            10.14293/PR2199.001131.v2
            e562a687-d436-4e13-b5fa-9c1f0e16c0c4

            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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