QUANTUM FIELDS ON CURVED MOMENTUM SPACE

Abstract

Relativistic particles with momentum space described by a group manifold provide a very interesting link between gravity, quantum group symmetries and non-commutative field theories. We discuss how group valued momenta emerge in the context of three-dimensional Einstein gravity and describe the related non-commutative field theory. As an application we introduce a non-commutative heat-kernel, calculate the associated spectral dimension and comment on its non-trivial behavior. In four spacetime dimensions the only known example of momenta living on a group manifold is encountered in the context of the κ-Poincaré algebra introduced by Lukierski et al. 20 years ago. I will discuss the construction of a one-particle Hilbert space from the classical κ-deformed phase space and show how the group manifold structure of momentum space leads to an ambiguity in the quantization procedure. The tools introduced in the discussion of field quantization lead to a natural definition of deformed two-point function.