Research Article
A Representation of an Octonionic Interaction of Color Quarks with the Application of Feynman Diagram
Arun Kumar Rathore*
,
Bhupesh Chandra Chanyal
Issue:
Volume 14, Issue 2, April 2025
Pages:
44-51
Received:
21 January 2025
Accepted:
20 February 2025
Published:
3 March 2025
DOI:
10.11648/j.ajmp.20251402.11
Downloads:
Views:
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.
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 connecti...
Show More
