Abstract
Lie-isotopic and Lie-admissible theories are based on non-trivial realisation and generalisation of the conventional product and Lie algebra. Various studies are now performed in applying this formalism to metric spaces, gauge theory, classical and quantum mechanics, field theory, and quantum groups. Lie-isotopic construction provides consistentgeneralisations of Hamiltonian mechanics refered to as Birkhofflan mechanics and Birkhoff-Santilli mechanics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D.I. Blokhintsev, Phys. Lett. 12: 272 (1964).
L.B. Redei. Phys. Rev. 145: 999 (1966).
H.B. Nielsen and I. Picek, Phys. Lett. B144: 141 (1982).
B.H. Aronson, G.J. Bock, H-Y. Cheng, and E. Fischbach, Phys. Rev. D28: 476 (1983).
B.H. Aronson, G.J. Bock, H-Y. Cheng, and E. Fischbach, Phys. Rev. D28: 495 (1983).
A.K. Aringazin, Hadronic J. 12: 71 (1989).
F. Cardone, R. Mignani, and R.M. Santilli, J. Phys. G18: L61 (1992).
N. Grossman et al, Phys. Rev. Lett. 59: 18 (1987).
M. Gasperini, Phys. Lett. B177: 51 (1986).
M. Gasperini, Phys. Rev. D33: 3594 (1986); Phys. Lett. B163: 84 (1985).
M. Gasperini, Phys. Lett. B141: 364 (1984).
M. Gasperini, Phys. Rev. D33: 3594 (1986); Mod. Phys. Lett. A2: 385 (1987); Class Quantum Grav. 4: 485 (1987).
M. Gasperini, Nuovo Cimento B81: 7 (1984); Hadronic J. 7: 234, 650, 971 (1984).
M. Gasperini, Nuovo Cimento A83: 309 (1984).
J. Ellis, M. Gaillard, D. Nanopoulos, and S. Rudaz, Nucl. Phys. B176: 61 (1980).
A. Zee, Phys. Rev. D25: 1864 (1982).
N. Rosen, Astrophys. J. 297: 347 (1985).
A.K. Aringazin and G.S. Asanov, Gen. Rel. Grav. 17: 1153 (1985).
A.K. Aringazin and G.S. Asanov, Rep. Math. Phys. 25: 183 (1988).
H. Rund, “The Differential Geometry of Finsler Spaces,” Springer, Berlin (1959)
G.S. Asanov, “Finsler Geometry, Relativity and Gauge Theories,” D.Reidel, Dordrecht(1985).
M. Matsumoto, “Foundations of Finsler Geometry and Special Finsler Spaces,” Diseisha Press, Kaiseisha (1986).
G.S. Asanov and S.P. Ponomarenko, “Finsler Fiber Bundle Over Space-Time, Associated Gauge Fields and Connections”Stiinca, Kishinev (1989).
A.K. Aringazin and A.L. Mikhailov, Class, and Quantum Grav.8: 1685 (1991).
R.M. Santilli, “Foundations of Theoretical Mechanics,” Vol.11, Springer, New York (1983).
R.M. Santilli, “Isotopic Generalization of Galilei’s and Einstein’s Relativities,” Vols. I, II, Hadronic Press, Palm Harbor (1991).
J. Kadeisvili, “Santilli’s Isotopies of Contemporary Algebras, Geometries and Relativities,” Hadronic Press, Palm Harbor (1992).
A.K. Aringazin, A. Jannussis, D.F. Lopez, M. Nishioka, and B. Veljanoski, “Santilli’s LieIsotopic Generalization of Galilei’s and Einstein’s Relativities,” Kostarakis Publishers, Athens (1991).
A.K. Aringazin, A. Jannussis, D.F. Lopez, M. Nishioka, and B. Veljanoski, Algebras, Groups and Geometries 7: 211 (1990).
R.M. Santilli, Lett. Nuovo Cimento 37: 545 (1983).
R.M. Santilli, Hadronic J. 8: 25, 36 (1985).
G.Yu. Bogoslovski, Nuovo Cimento B40: 116 (1977); B43: 377 (1978).
C.M. Will, “Theory and Experiment in Gravitational Physics,” Cambridge Univ. Press, London (1981).
S. Ikeda, J. Math. Phys. 26: 958 (1985); Nuovo Cimento B100: 493 (1987).
E. Witten, Nucl. Phys. B186: 412 (1981); S.Randjbar-Daemi, A.Salam, and J.Strathdee, Nucl. Phys. B214: 491 (1983).
S. Weinberg, Phys. Lett. B125: 265 (1983).
M. Chaichian, A.P. Demichev, and N.F. Nelipa, Phys. Lett. B169: 327 (1986.
M.B. Green, J.H. Schwarz, and E. Witten, “Superstring Theory,” Cambridge Univ. Press, Cambridge (1987).
W. Siegel, “Introduction to String Theory,” World Sci., Singapore (1988).
A.M. Polyakov, “Gauge Fields and Strings,” Harwood Academic Publ., Chur (1987).
E. Witten, Preprint IASSNS-HEP-88/32 (1988).
M. Gasperini, Hadronic J. 6: 935, 1462 (1983); M.Nishioka, Hadronic J. 7: 1636 (1984).
A. Jannussis, G. Brodimas, and R. Mignani, J. Phys. A24: L775 (1991).
“Proc. of the Third Workshop on Lie-Admissible Formulations,” Hadronic Press, Nonantum (1981); “Proc. of the First Intern. Confer. on Non-Potential Interactions and Their Lie-Admissible Treatment,” Hadronic Press, Nonantum (1982).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this chapter
Cite this chapter
Aringazin, A.K., Aringazin, K.M. (1994). Universality of the Lie-Isotopic Symmetries for Deformed Minkowskian Metrics. In: Barone, M., Selleri, F. (eds) Frontiers of Fundamental Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2560-8_18
Download citation
DOI: https://doi.org/10.1007/978-1-4615-2560-8_18
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6093-3
Online ISBN: 978-1-4615-2560-8
eBook Packages: Springer Book Archive