J Madore 1992 Class. Quantum Grav. 9 69 doi:10.1088/0264-9381/9/1/008
J Madore
Show affiliationsA model of Euclidean spacetime is presented in which at scales less than a certain length kappa the notion of a point does not exist. At scales larger then kappa the model resembles the 2-sphere S2. The algebra which determines the structure of the model, and which replaces the algebra of functions, is an algebra of matrices. The order of n of the matrices is connected with the length kappa and the radius r of the sphere by the relation kappa approximately r/n. The elements of differential calculus are sketched as well as the possible definitions of a metric and linear connection. A definition of the path integral is given and a few examples of field theory on a fuzzy sphere are finally referred to.
04.62.+v Quantum fields in curved spacetime
81T20 Quantum field theory on curved space backgrounds
83C75 Space-time singularities, cosmic censorship, etc.
15A30 Algebraic systems of matrices (See also 16S50, 20Gxx, 20Hxx)
58D30 Applications (in quantum mechanics (Feynman path integrals), relativity, fluid dynamics, etc.)
Issue 1 (January 1992)
J Madore 1992 Class. Quantum Grav. 9 69
K Shiraishi and S Hirenzaki 1992 Class. Quantum Grav. 9 2277
A Dimakis and F Muller-Hoissen 1991 Class. Quantum Grav. 8 2093
A Higuchi 1991 Class. Quantum Grav. 8 2023
K Shiraishi 1990 Class. Quantum Grav. 7 135
K Shiraishi 1989 Class. Quantum Grav. 6 2029
A Higuchi 1987 Class. Quantum Grav. 4 721
P G Grove 1986 Class. Quantum Grav. 3 801
R Aurich and S Lustig 2011 Class. Quantum Grav. 28 085017
Teruki Hanada et al 2010 Class. Quantum Grav. 27 225010