Noncommutative field theory on $\mathbb{R}^3_λ$

Abstract

We consider the noncommutative space $\mathbb{R}^3_λ$, a deformation of the algebra of functions on $\mathbb{R}^3$ which yields a foliation of $\mathbb{R}^3$ into fuzzy spheres. We first review the construction of a natural matrix basis adapted to $\mathbb{R}^3_λ$. 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.

12 pages. Conference proceedings. Presented at the workshop "Noncommutative Field theory and Gravity" Corfu 2013