Fuzzy Non-Trivial Gauge Configurations

In this talk we will report on few results of discrete physics on the fuzzy sphere . In particular non-trivial field configurations such as monopoles and solitons are constructed on fuzzy S using the language of K-theory , i.e projectors . As we will show , these configurations are intrinsically finite dimensional matrix models . The corresponding monopole charges and soliton winding numbers are also found using the formalism of noncommutative geometry and cyclic cohomology . Fuzzy physics is aimed to be an alternative method to approach discrete physics . Problems of lattice physics especially those with topological roots are all avoided on fuzzy spaces . For example , chiral anomaly , Fermion doubling and the discretization of non-trivial topological field configurations were all formulated consistently on the fuzzy sphere [see [1] and the extensive list of references therein] . The paradigm of fuzzy physics is “discretization by quantization“, namely given a space , we treat it as a phase space and then quantize it . This requires the existence of a symplectic structure on this space . One such class of spaces which admit symplectic forms are the co-adjoint orbits, for example CP = S , CP , CP and so on . Their quantization to obtain their fuzzy counterparts is done explicitly in [2, 1] . Here we will only summarize the important results for S which are needed for the purpose of this paper . 1 Fuzzy S Fuzzy S or SF is the algebra A = Mat2l+1 of (2l + 1)×(2l + 1) matrices which is generated by the operators ni , i = 1, 2, 3 , which are defined by ni = Li