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SMOOTH LOOPS AND FIBER BUNDLES: THEORY OF PRINCIPAL Q-BUNDLES

ALEXANDER I. NESTEROV

Departamento de Física, CUCEI, Universidad de Guadalajara, Av. Revolución 1500, Guadalajara, CP 44420, Jalisco, México

https://doi.org/10.1142/S0219887809003412Cited by:2 (Source: Crossref)

Abstract

A nonassociative generalization of the principal fiber bundles with a smooth loop mapping on the fiber is presented. Our approach allows us to construct a new kind of gauge theories that involve higher "nonassociative" symmetries.

Keywords:

AMSC: 81S99, 55R65, 53Z05, 57R20

References

R. Jackiw, Phys. Rev. Lett. 54, 159 (1985), DOI: 10.1103/PhysRevLett.54.159. Crossref, Web of Science, Google Scholar
D. G. Boulware, S. Deser and B. Zumino, Phys. Lett. B 153, 307 (1985). Crossref, Web of Science, Google Scholar
B. Grossman, Phys. Lett. B 152, 93 (1985). Crossref, Web of Science, Google Scholar
B. Grossman, Phys. Rev. D 33, 2922 (1985), DOI: 10.1103/PhysRevD.33.2922. Crossref, Web of Science, Google Scholar
Y.-S. Wu and A. Zee, Phys. Lett. B 152, 98 (1985). Crossref, Web of Science, Google Scholar
A. I. Nesterov, Phys. Lett. A 328, 110 (2004), DOI: 10.1016/j.physleta.2004.06.024. Crossref, Web of Science, Google Scholar
A. I. Nesterov, Int. J. Geom. Meth. Mod. Phys. 4, 717 (2007), DOI: 10.1142/S0219887807002259. Link, Web of Science, Google Scholar
A. I. Nesterov and F. Aceves de la Cruz, Phys. Lett. A 302, 253 (2002), DOI: 10.1016/S0375-9601(02)01172-6. Crossref, Web of Science, Google Scholar
A. I. Nesterov , Non Associative Algebra and Its Applications , eds. R. Costa et al. ( Marcel Dekker , New York , 2000 ) . Google Scholar
A. I. Nesterov, Methods of nonassociative algebra in physics, Dr. Sci. Dissertation, Krasnoyarsk State University, Krasnoyarsk (1989) . Google Scholar
T. Strobl, Phys. Rev. Lett. 93, 211601–1 (2004), DOI: 10.1103/PhysRevLett.93.211601. Google Scholar
S. Ramgoolam, JHEP 0403, 034 (2004). Google Scholar
P. de Medeiros and S. Ramgoolam, JHEP 03, 072 (2005). Google Scholar
A. I. Mal'cev, Mat. Sb. 36, 569 (1955). Google Scholar
A. L. Carey, Phys. Lett. B 194, 267 (1987). Crossref, Web of Science, Google Scholar
S.-G. Jo, Phys. Lett. B 163, 353 (1985). Crossref, Web of Science, Google Scholar
A. J. Niemi and G. W. Semenoff, Phys. Rev. Lett. 55, 927 (1985), DOI: 10.1103/PhysRevLett.55.927. Crossref, Web of Science, Google Scholar
G. W. Semenoff, Phys. Rev. Lett. 60, 680 (1988), DOI: 10.1103/PhysRevLett.60.680. Crossref, Web of Science, Google Scholar
A. I. Nesterov, Int. J. Theor. Phys. 40, 339 (2001), DOI: 10.1023/A:1003760016797. Crossref, Web of Science, Google Scholar
A. I. Nesterov, Phys. Rev. D 56, R7498 (1997), DOI: 10.1103/PhysRevD.56.R7498. Crossref, Web of Science, Google Scholar
A. I. Nesterov, Phys. Lett. A 250, 55 (1998), DOI: 10.1016/S0375-9601(98)00768-3. Crossref, Web of Science, Google Scholar
A. I. Nesterov and L. V. Sabinin, Phys. Rev. D 62, 081501–1 (2000), DOI: 10.1103/PhysRevD.62.081501. Crossref, Web of Science, Google Scholar
A. I. Nesterov and L. V. Sabinin, Comment. Math. Univ. Carol. 41(2), 347 (2000). Google Scholar
A. I. Nesterov and L. V. Sabinin, Hadron. J. 20, 219 (1997). Google Scholar
A. I. Nesterov and L. V. Sabinin, Int. J. Theor. Phys. 36, 1981 (1997), DOI: 10.1007/BF02435954. Crossref, Web of Science, Google Scholar
A. A. Ungar, J. Math. Phys. 35, 1408 (1991), DOI: 10.1063/1.530597. Crossref, Web of Science, Google Scholar
A. A. Ungar, Am. J. Phys. 59, 824 (1991), DOI: 10.1119/1.16730. Crossref, Web of Science, Google Scholar
P. Kuusk, J. Örd and E. Paal, J. Math. Phys. 35, 321 (1994), DOI: 10.1063/1.530773. Crossref, Web of Science, Google Scholar
V. D. Belousov , Foundations of the Theory of Quasigroups and Loops ( Nauka , Moscow , 1967 ) . Google Scholar
R. H. Bruck , A Survey of Binary Systems ( Springer-Verlag , Berlin , 1971 ) . Crossref, Google Scholar
H. Pflugfelder , Quasigroups and Loops: An Introduction ( Heldermann Verlag , Berlin , 1990 ) . Google Scholar
O. Chein , H. Pflugfelder and J. D. H. Smith (eds.) , Quasigroups and Loops: Theory and Applications ( Heldermann Verlag , Berlin , 1990 ) . Google Scholar
L. V. Sabinin , Smooth Quasigroups and Loops ( Kluwer Academic Publishers , Dordrecht , 1999 ) . Crossref, Google Scholar
S. N. Hudson, Trans. Amer. Math. Soc. 115, 417 (1965), DOI: 10.2307/1994278. Crossref, Web of Science, Google Scholar
S. N. Hudson, Trans. Amer. Math. Soc. 118, 526 (1965), DOI: 10.2307/1993976. Crossref, Web of Science, Google Scholar
L. V. Sabinin , Differential equations of smooth loops , Proceedings of Seminar on Vector and Tensor Analysis 23 ( Moscow Univ. , Moscow , 1988 ) . Google Scholar
L. V. Sabinin, Russian Math. Survey 49, 172 (1989), DOI: 10.1070/RM1994v049n02ABEH002227. Crossref, Web of Science, Google Scholar
L. V. Sabinin, Proc. Inst. Math. Siberian Branch Ac. Sci. USSR 14, 208 (1994). Google Scholar
I. A. Batalin, J. Math. Phys. 22, 1837 (1981), DOI: 10.1063/1.525155. Crossref, Web of Science, Google Scholar
M. Nakahara , Geometry, Topology and Physics ( IOP , London , 1990 ) . Crossref, Google Scholar
S. K. Kobayashi and K. Nomizy , Foundations of Differential Geometry I ( Interscience Publisher , New York , 1963 ) . Google Scholar