Noncommutative field theory on ℝ³_λ

Abstract

Abstract We consider the noncommutative space ℝ 3 λ , a deformation of the algebra of functions on ℝ 3 which yields a foliation of ℝ 3 into fuzzy spheres. We first review the construction of a natural matrix basis adapted to ℝ 3 λ . We thus consider the problem of defining a new Laplacian operator for the deformed algebra. We propose an operator which is not of Jacobi type. The implication for field theory of the new Laplacian is briefly discussed.