Revisiting the role of octonions in hadronic physics
Tóm tắt
Octonions and their split versions are shown to be applicable to the solutions of a large number of problems in hadronic physics, from the foundations of exceptional groups that are used in grand unified theories, to heterotic strings, to the non-Desarguesian geometric property of space-time symmetries, twistors, harmonic superspace, conformal field theories, etc. Upon a brief review of these investigations we proceed to show how they are used in the unification of ancient and modern geometries, which in turn open new avenues for, and goes far beyond in providing, geometric foundations for the existence of internal symmetries such as color and flavor.
Tài liệu tham khảo
A. Galperin, E. Ivanov, V. Ogievetsky, and E. Sokatchev, Ann. Phys. Rev. 185 (1988).
M. Evans, F. Gursey, and V. Ogievetsky, Phys. Rev. D 47, 3496 (1993).
M. J. Duff, J. M. Evans, R. R. Khuri, J. X. Lu, and R. Minasian, Phys. Rev. B 412, 281 (1997).
P. Ramond, Phys. Rev. D: Part. Fields 3, 2415 (1971).
A. Neveu and J. Schwarz, Nucl. Phys. B 31, 86 (1971).
T. A. Golfand and E. P. Likhtman, JETP Lett. 13, 323 (1971).
D. V. Volkov and V. P. Akulov, Phys. Lett. B 46, 109 (1973).
J. Wess and B. Zumino, Nucl. Phys. B 70, 39 (1974), Phys. Lett. B 49, 52 (1974).
A. de Rujula, H. Georgi, and S. L. Glashow, Phys. Rev. D: Part. Fields 12, 147 (1975).
D. B. Lichtenberg, W. Namgung, E. Predazzi, and J. G. Wills, Phys. Lett. 48, 1653 (1982)
W. Namgung and D. B. Lichtenberg, Lett. Nuovo Cim. 41, 597 (1984)
A. Martin, Z. Phys. C 32, 359 (1986), Symmetry in Nature (Scuola Normale Superiore, Pisa,1989), Vol. 2, p. 523.
M. Anselmino, E. Predazzi, S. Ekelin, S. Fredriksson, and D. B. Lichtenberg, Rev. Mod. Phys. 65, 1199 (1993).
S. Catto and F. Gursey, Nuovo Cim. A 86, 201 (1985).
T. Eguchi, Phys. Lett. B 59, 457 (1975).
I. Bars and A. J. Hanson, Phys. Rev. D: Part. Fields 13, 1744 (1976).
K. Johnson and C. B. Thorn, Phys. Rev. D: Part. Fields 13, 1934 (1976).
S. Catto and F. Gürsey, Nuovo Cim. A 99, 685 (1988).
S. Catto, Y. Gürcan, A. Khalfan, and L. Kurt, J. Phys. 670, 012016 (2016).
M. Günaydin and F. Gürsey, J. Math. Phys. 14, 1651 (1973).
S. Okubo, Introduction to Octonion and other Nonassociative Algebras in Physics, vol. 2 of Montroll Memorial Lecture Series in Mathematical Physics (Cambridge Univ. Press, Cambridge, 1995).
J. Baez, Bull. Am. Math. Soc. 39, 145–205 (2002).
S. Catto, “Exceptional projective geometries and internal symmetries,” arXiv:hep-th/0302079.
P. S. Bisht, B. C. Chanyal, and O. S. Negi, Int. J. Theor. Phys. 49, 1333 (2010), Int. J. Theor. Phys. 50, 1919 (2011), Int. J. Theor. Phys. 51, 3410 (2012), Int. J. Theor. Phys. 52, 3522 (2013), Int. J. Theor. Phys. 54, 3532 (2015).