The ultraviolet-finite Hamiltonian approach on the noncommutative Minkowski space

TL;DR

This paper presents a Hamiltonian approach to noncommutative Minkowski space that yields an ultraviolet-finite S-matrix by modifying the limit of coinciding points and defining regularized field monomials.

Contribution

It introduces a novel Hamiltonian formalism on noncommutative Minkowski space that achieves ultraviolet finiteness in quantum field theory.

Findings

Ultraviolet divergences are eliminated in the S-matrix.

Regularized field monomials enable well-defined interaction terms.

The approach provides a consistent framework for noncommutative field theory.

Abstract

This is an exposition of joint work with S. Doplicher, K. Fredenhagen, and G. Piacitelli on field theory on the noncommutative Minkowski space. The limit of coinciding points is modified compared to ordinary field theory in a suitable way which allows for the definition of so-called regularized field monomials as interaction terms. Employing these in the Hamiltonian formalism results in an ultraviolet finite S-matrix.