Research PapersNo Access

AN INVARIANT APPROACH TO DYNAMICAL FUZZY SPACES WITH A THREE-INDEX VARIABLE

NAOKI SASAKURA

Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

https://doi.org/10.1142/S0217732306020329Cited by:18 (Source: Crossref)

Abstract

A dynamical fuzzy space might be described by a three-index variable , which determines the algebraic relations among the functions f_a on the fuzzy space. A fuzzy analogue of the general coordinate transformation would be given by the general linear transformation on f_a. We study equations for the three-index variable invariant under the general linear transformation and show that the solutions can be generally constructed from the invariant tensors of Lie groups. As specific examples, we study SO(3) symmetric solutions and discuss the construction of a scalar field theory on a fuzzy two-sphere within this framework.

Keywords:

PACS: 11.10.Nx

References

L. J. Garay, Int. J. Mod. Phys. A 10, 145 (1995). Link, Web of Science, ADS, Google Scholar
T. Yoneya, Prog. Theor. Phys. 103, 1081 (2000). Crossref, Web of Science, Google Scholar
H. Salecker and E. P. Wigner, Phys. Rev. 109, 571 (1958). Crossref, Web of Science, ADS, Google Scholar
F. Karolyhazy, Nuovo Cimento A 42, 390 (1966). Crossref, Web of Science, ADS, Google Scholar
Y. J. Ng and H. Van Dam, Mod. Phys. Lett. A 9, 335 (1994). Web of Science, ADS, Google Scholar
G. Amelino-Camelia, Mod. Phys. Lett. A 9, 3415 (1994). Link, Web of Science, ADS, Google Scholar
N. Sasakura, Prog. Theor. Phys. 102, 169 (1999). Crossref, Web of Science, ADS, Google Scholar
A. Connes , Noncommutative Geometry ( Academic Press , 1994 ) . Google Scholar
J. Madore , An Introduction to Noncommutative Differential Geometry and Physical Applications , London Mathematical Society Lecture Note Series 257 ( Cambridge Univ. Press , 2000 ) . Google Scholar
G. Landi, hep-th/9701078 . Google Scholar
N. Sasakura, JHEP 0401, 016 (2004). ADS, Google Scholar
N. Sasakura, Class. Quantum Grav. 21, 3593 (2004). Crossref, Web of Science, ADS, Google Scholar
N. Sasakura, Phys. Lett. B 599, 319 (2004). Crossref, Web of Science, ADS, Google Scholar
A. Messiah , Quantum Mechanics ( North-Holland , 1962 ) . Google Scholar
D. A. Varshalovich , A. N. Moskalev and V. K. Khersonsky , Quantum Theory of Angular Momentum ( World Scientific , 1988 ) . Link, Google Scholar
J. Madore, Class. Quantum Grav. 9, 69 (1992). Crossref, Web of Science, ADS, Google Scholar
B. P. Dolan, D. O'Connor and P. Presnajder, JHEP 0402, 055 (2004). ADS, Google Scholar
S. Ramgoolam, JHEP 0403, 034 (2004). ADS, Google Scholar
P. de Medeiros and S. Ramgoolam, JHEP 0503, 072 (2005). ADS, Google Scholar
P. Aschieriet al., JHEP 0404, 034 (2004). ADS, Google Scholar
P. Aschieriet al., Fortsch. Phys. 52, 718 (2004). Crossref, Web of Science, ADS, Google Scholar
P. Aschieri, J. Madore, P. Manousselis and G. Zoupanos, hep-th/0503039 . Google Scholar