A Representation of an Octonionic Interaction of Color Quarks with the Application of Feynman Diagram

Arun Kumar Rathore; Bhupesh Chandra Chanyal

doi:doi:10.11648/j.ajmp.20251402.11

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A Representation of an Octonionic Interaction of Color Quarks with the Application of Feynman Diagram

Arun Kumar Rathore^*

, Bhupesh Chandra Chanyal

Published in American Journal of Modern Physics (Volume 14, Issue 2)

Received: 21 January 2025 Accepted: 20 February 2025 Published: 3 March 2025

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Abstract

The SU(3) flavour symmetry for quarks and antiquarks has been demonstrated via the complexified octonion space, where the six complex octonion operators are essentially identical to the SL(3,C) group generators. It has been developed an extensive analysis of the quark flavour theory in the context of complex-octonion space by analyzing the connection between octonions and the SU(3) group. Therefore, it is argued that the extended theory of quark flavors, which preserves the property of non-commutativity, is the complexified variant of octonions. This theoretical model may be further extended to the SU(3) color symmetry, which is regarded as an exact symmetry. In this work, to gain a complete understanding of quark color theory in the framework of complex octonionic space, we have derived the relationship between octonions and the SU(3)c color group. It has been studied that only eight possibilities of paired gluons are available to provide colorless states of hadrons in order to represent theoretically the octonion glueballs. With the help of Feynman diagrams, we examined the octonionic interaction of color quarks (such as quark-quark, quark anti-quark, and anti-quarks anti-quarks interactions). For the interactions, we have obtained the complex octonion algebraic form of the interaction term, propagator, vertex factor, and color factor. Most importantly, we have examined the conditions for valid and invalid interactions for the complex-octonion formalism.

Published in	American Journal of Modern Physics (Volume 14, Issue 2)
DOI	10.11648/j.ajmp.20251402.11
Page(s)	44-51
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Octonion Algebra, Complex Octonion Space, Quark Color, Feynmann Diagram, SU(3) Color Group

References

[1]	Dickson, L. E. On quaternions and their generalization and the history of the eight square theorem. Annals of Mathematics. 1919, 20(3), 155-171. https://doi.org/10.2307/1967865
[2]	P. G. Tait, “An elementary Treatise on Quaternions”, Ed. 3, Cambridge Univ. Press (1875).
[3]	Cayley, A. On Jacobi’s Elliptic functions, in reply to the Rev. Brice Bronwin; and on Quaternions: To the editors of the Philosophical Magazine and Journal. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 1845, 26(172), 208-211.
[4]	Günaydin, M., & Gürsey, F. Quark structure and octonions. Journal of Mathematical Physics. 1973, 14(11), 1651-1667. https://doi.org/10.1063/1.16662 40
[5]	Günaydin, M., & Gürsey, F. Quark statistics and octonions. Physical Review D. 1974, 9(12), 3387. https://doi.org/10.1103/PhysRevD.9.3387
[6]	O’Neill, C. Octonions, the three flavours of matter and new kind of super-symmetry. Canadian Journal of Pure & Applied Sciences. 2021, 15(2), 5261-5268.
[7]	Pushpa, Bisht, P. S., Li, T., & Negi, O. P. S. Quaternion octonion reformulation of quantum chromodynamics. International Journal of Theoretical Physics. 2011, 50, 594-606.
[8]	Pushpa, Bisht, P. S., Li, T., & Negi, O. P. S. Quaternion- Octonion SU (3) Flavor Symmetry. International Journal of Theoretical Physics. 2012, 51, 1866-1875. https://doi.org/10.1007/s10773-011-1062-x
[9]	Weng, Z. H. Color Confinement and Spatial Dimensions in the Complex-Sedenion Space. Advances in Mathematical Physics. 2017, 2017(1), 9876464- 9876490.
[10]	Chanyal, B. C., Bisht, P. S., Li, T., & Negi, O. P. S. Octonion quantum chromodynamics. International Journal of Theoretical Physics. 2012, 51, 3410-3422.
[11]	Chanyal, B. C., Sharma, V. K., & Negi, O. P. S. Octonionic gravi-electromagnetism and dark matter. International Journal of Theoretical Physics. 2015, 54, 3516-3532.
[12]	Wang, H., & Bian, X. The right inverse of Dirac operator in octonionic space. Journal of Geometry and Physics. 2017, 119, 139-145.
[13]	S. Catto, Y. Gürcan, A. Khalfan, and Kurt, L. . Algebraic formulation of hadronic supersymmetry based on octonions: new mass formulas and further applications. J. Phys. Conf. Ser. 2014, 563, 012006.
[14]	Chanyal, B. C. On octonion quark confinement condition. Modern Physics Letters A. 2021, 36(37), 2150264. https://doi.org/10.1142/S0217732321502643
[15]	Joshi, D. C. Introduction to Quantum Electrodynamics and Particle Physics. I. K. International Publishing House Pvt. Ltd. New Delhi, India. 2006, pp 126-129.
[16]	Rathore, A. K., Sharma, V. K., & Chanyal, B.C. Complex octonion-based SU (3) flavor symmetry with the concept of octet representation for quark composite particles. The European Physical Journal Plus. 2024, 139(3), 210. https://doi.org/10.1140/epjp/s13360-024-05021-5
[17]	Chanyal, B. C., & Pathak, M. Quaternionic approach to dual magnetohydrodynamics of dyonic cold plasma. Advances in High Energy Physics. 2018, 2018(1), 7843730-7843743. https://doi.org/10.1155/2018/7843730
[18]	Chanyal, B. C. A relativistic quantum theory of dyons wave propagation. Canadian Journal of Physics. 2017, 95(12), 1200-1207. https://doi.org/10.1139/cjp-2017-0080
[19]	Chanyal, B. C., Bisht, P. S., & Negi, O. P. S. Generalized octonion electrodynamics. International Journal of Theoretical Physics. 2010, 49, 1333-1343.
[20]	Weng, Z. H. Color Confinement and Spatial Dimensions in the Complex-Sedenion Space. Advances in Mathematical Physics. 2017, 2017(1), 9876464- 9876491.
[21]	Wang, H., & Bian, X. The right inverse of Dirac operator in octonionic space. Journal of Geometry and Physics. 2017, 119, 139-145.
[22]	Weng, Z. H. Torques and angular momenta of fluid elements in the octonion spaces. Mathematical Methods in the Applied Sciences. 2023, 46(5), 5810-5820.
[23]	Weng, Z. H. Some spin textures relevant to magnetic moments in the octonion spaces. AIP Advances. 2023, 13(8), 085016.
[24]	Weng, Z. H. Conservedquantitiesofvectorialmagnitudes within the material media. International Journal of Modern Physics A. 2023, 38(01), 2350001.
[25]	Furey, C. Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra. Physics Letters B. 2018, 785, 84-89.
[26]	Kugo, T., & Townsend, P. Supersymmetry and the division algebras. Nuclear Physics B. 1983, 221(2), 357- 380.
[27]	Chanyal, B. C. Octonion generalization of Pauli and Dirac matrices. International Journal of Geometric Methods in Modern Physics. 2015, 12(01), 1550007- 1550031.
[28]	Marques-Bonham, S., Chanyal, B. C., & Matzner, R. Yang–Mills-like field theories built on division quaternion and octonion algebras. The European Physical Journal Plus. 2020, 135(608), 1-34. https://doi.org/10.1140/epjp/s13360-020-00626-y
[29]	Chanyal, B. C. Octonion symmetric Dirac-Maxwell equations. Turkish Journal of Physics. 2014, 38(2), 174- 186. https://doi.org/10.3906/fiz-1401-14
[30]	Chanyal, B. C. Octonionic matrix representation and electromagnetism. Journal of the Korean Physical Society. 2014, 65, 1715-1728.
[31]	Chanyal, B. C., Bisht, P. S., & Negi, O. P. S. Octonion and conservation laws for dyons. International Journal of Modern Physics A. 2013, 28(26), 1350125.

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APA Style

Rathore, A. K., Chanyal, B. C. (2025). A Representation of an Octonionic Interaction of Color Quarks with the Application of Feynman Diagram. American Journal of Modern Physics, 14(2), 44-51. https://doi.org/10.11648/j.ajmp.20251402.11

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ACS Style

Rathore, A. K.; Chanyal, B. C. A Representation of an Octonionic Interaction of Color Quarks with the Application of Feynman Diagram. Am. J. Mod. Phys. 2025, 14(2), 44-51. doi: 10.11648/j.ajmp.20251402.11

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AMA Style

Rathore AK, Chanyal BC. A Representation of an Octonionic Interaction of Color Quarks with the Application of Feynman Diagram. Am J Mod Phys. 2025;14(2):44-51. doi: 10.11648/j.ajmp.20251402.11

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@article{10.11648/j.ajmp.20251402.11,
  author = {Arun Kumar Rathore and Bhupesh Chandra Chanyal},
  title = {A Representation of an Octonionic Interaction of Color Quarks with the Application of Feynman Diagram},
  journal = {American Journal of Modern Physics},
  volume = {14},
  number = {2},
  pages = {44-51},
  doi = {10.11648/j.ajmp.20251402.11},
  url = {https://doi.org/10.11648/j.ajmp.20251402.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20251402.11},
  abstract = {The SU(3) flavour symmetry for quarks and antiquarks has been demonstrated via the complexified octonion space, where the six complex octonion operators are essentially identical to the SL(3,C) group generators. It has been developed an extensive analysis of the quark flavour theory in the context of complex-octonion space by analyzing the connection between octonions and the SU(3) group. Therefore, it is argued that the extended theory of quark flavors, which preserves the property of non-commutativity, is the complexified variant of octonions. This theoretical model may be further extended to the SU(3) color symmetry, which is regarded as an exact symmetry. In this work, to gain a complete understanding of quark color theory in the framework of complex octonionic space, we have derived the relationship between octonions and the SU(3)c color group. It has been studied that only eight possibilities of paired gluons are available to provide colorless states of hadrons in order to represent theoretically the octonion glueballs. With the help of Feynman diagrams, we examined the octonionic interaction of color quarks (such as quark-quark, quark anti-quark, and anti-quarks anti-quarks interactions). For the interactions, we have obtained the complex octonion algebraic form of the interaction term, propagator, vertex factor, and color factor. Most importantly, we have examined the conditions for valid and invalid interactions for the complex-octonion formalism.},
 year = {2025}
}

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TY  - JOUR
T1  - A Representation of an Octonionic Interaction of Color Quarks with the Application of Feynman Diagram
AU  - Arun Kumar Rathore
AU  - Bhupesh Chandra Chanyal
Y1  - 2025/03/03
PY  - 2025
N1  - https://doi.org/10.11648/j.ajmp.20251402.11
DO  - 10.11648/j.ajmp.20251402.11
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 44
EP  - 51
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20251402.11
AB  - The SU(3) flavour symmetry for quarks and antiquarks has been demonstrated via the complexified octonion space, where the six complex octonion operators are essentially identical to the SL(3,C) group generators. It has been developed an extensive analysis of the quark flavour theory in the context of complex-octonion space by analyzing the connection between octonions and the SU(3) group. Therefore, it is argued that the extended theory of quark flavors, which preserves the property of non-commutativity, is the complexified variant of octonions. This theoretical model may be further extended to the SU(3) color symmetry, which is regarded as an exact symmetry. In this work, to gain a complete understanding of quark color theory in the framework of complex octonionic space, we have derived the relationship between octonions and the SU(3)c color group. It has been studied that only eight possibilities of paired gluons are available to provide colorless states of hadrons in order to represent theoretically the octonion glueballs. With the help of Feynman diagrams, we examined the octonionic interaction of color quarks (such as quark-quark, quark anti-quark, and anti-quarks anti-quarks interactions). For the interactions, we have obtained the complex octonion algebraic form of the interaction term, propagator, vertex factor, and color factor. Most importantly, we have examined the conditions for valid and invalid interactions for the complex-octonion formalism.
VL  - 14
IS  - 2
ER  -

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Author Information

Arun Kumar Rathore

Department of Physics, G. B. Pant University of Agriculture and Technology, Pantnagar, India

Contact Email

http://orcid.org/0009-0007-3621-5088
Bhupesh Chandra Chanyal

Department of Physics, G. B. Pant University of Agriculture and Technology, Pantnagar, India

Contact Email

http://orcid.org/0000-0003-3652-1601

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Plain Text BibTeX RIS

APA Style

Rathore, A. K., Chanyal, B. C. (2025). A Representation of an Octonionic Interaction of Color Quarks with the Application of Feynman Diagram. American Journal of Modern Physics, 14(2), 44-51. https://doi.org/10.11648/j.ajmp.20251402.11

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ACS Style

Rathore, A. K.; Chanyal, B. C. A Representation of an Octonionic Interaction of Color Quarks with the Application of Feynman Diagram. Am. J. Mod. Phys. 2025, 14(2), 44-51. doi: 10.11648/j.ajmp.20251402.11

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AMA Style

Rathore AK, Chanyal BC. A Representation of an Octonionic Interaction of Color Quarks with the Application of Feynman Diagram. Am J Mod Phys. 2025;14(2):44-51. doi: 10.11648/j.ajmp.20251402.11

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@article{10.11648/j.ajmp.20251402.11,
  author = {Arun Kumar Rathore and Bhupesh Chandra Chanyal},
  title = {A Representation of an Octonionic Interaction of Color Quarks with the Application of Feynman Diagram},
  journal = {American Journal of Modern Physics},
  volume = {14},
  number = {2},
  pages = {44-51},
  doi = {10.11648/j.ajmp.20251402.11},
  url = {https://doi.org/10.11648/j.ajmp.20251402.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20251402.11},
  abstract = {The SU(3) flavour symmetry for quarks and antiquarks has been demonstrated via the complexified octonion space, where the six complex octonion operators are essentially identical to the SL(3,C) group generators. It has been developed an extensive analysis of the quark flavour theory in the context of complex-octonion space by analyzing the connection between octonions and the SU(3) group. Therefore, it is argued that the extended theory of quark flavors, which preserves the property of non-commutativity, is the complexified variant of octonions. This theoretical model may be further extended to the SU(3) color symmetry, which is regarded as an exact symmetry. In this work, to gain a complete understanding of quark color theory in the framework of complex octonionic space, we have derived the relationship between octonions and the SU(3)c color group. It has been studied that only eight possibilities of paired gluons are available to provide colorless states of hadrons in order to represent theoretically the octonion glueballs. With the help of Feynman diagrams, we examined the octonionic interaction of color quarks (such as quark-quark, quark anti-quark, and anti-quarks anti-quarks interactions). For the interactions, we have obtained the complex octonion algebraic form of the interaction term, propagator, vertex factor, and color factor. Most importantly, we have examined the conditions for valid and invalid interactions for the complex-octonion formalism.},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - A Representation of an Octonionic Interaction of Color Quarks with the Application of Feynman Diagram
AU  - Arun Kumar Rathore
AU  - Bhupesh Chandra Chanyal
Y1  - 2025/03/03
PY  - 2025
N1  - https://doi.org/10.11648/j.ajmp.20251402.11
DO  - 10.11648/j.ajmp.20251402.11
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 44
EP  - 51
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20251402.11
AB  - The SU(3) flavour symmetry for quarks and antiquarks has been demonstrated via the complexified octonion space, where the six complex octonion operators are essentially identical to the SL(3,C) group generators. It has been developed an extensive analysis of the quark flavour theory in the context of complex-octonion space by analyzing the connection between octonions and the SU(3) group. Therefore, it is argued that the extended theory of quark flavors, which preserves the property of non-commutativity, is the complexified variant of octonions. This theoretical model may be further extended to the SU(3) color symmetry, which is regarded as an exact symmetry. In this work, to gain a complete understanding of quark color theory in the framework of complex octonionic space, we have derived the relationship between octonions and the SU(3)c color group. It has been studied that only eight possibilities of paired gluons are available to provide colorless states of hadrons in order to represent theoretically the octonion glueballs. With the help of Feynman diagrams, we examined the octonionic interaction of color quarks (such as quark-quark, quark anti-quark, and anti-quarks anti-quarks interactions). For the interactions, we have obtained the complex octonion algebraic form of the interaction term, propagator, vertex factor, and color factor. Most importantly, we have examined the conditions for valid and invalid interactions for the complex-octonion formalism.
VL  - 14
IS  - 2
ER  -

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