Ultraviolet Renormalization of the van Hove-Miyatake Model: an Algebraic and Hamiltonian Approach

TL;DR

This paper compares algebraic and Hamiltonian methods for ultraviolet renormalization of the van Hove-Miyatake scalar field, demonstrating their equivalence through analysis of ground states and dressing transformations.

Contribution

It introduces and compares two distinct renormalization approaches for the van Hove-Miyatake model, establishing their equivalence.

Findings

Algebraic and Hamiltonian approaches yield equivalent renormalization results.

Ground states of the dynamical map are key to the algebraic method.

Non-unitary dressing transformation is used in the Hamiltonian approach.

Abstract

In this short communication we discuss the ultraviolet renormalization of the van Hove-Miyatake scalar field, generated by any distributional source. An abstract algebraic approach, based on the study of a special class of ground states of the van Hove-Miyatake dynamical map is compared with an Hamiltonian renormalization that makes use of a non-unitary dressing transformation. The two approaches are proved to yield equivalent results.