Hamiltonian Renormalisation IV. Renormalisation Flow of D+1 dimensional free scalar fields and Rotation Invariance

TL;DR

This paper extends Hamiltonian Renormalisation to D-dimensional free scalar fields, providing explicit computations for D=2 and a criterion to verify the approach to rotational invariance at finite lattice resolution.

Contribution

It introduces a method to test for rotational invariance in the renormalisation flow of free scalar fields across multiple dimensions.

Findings

Explicit computations for D=2 case.

A criterion for rotational invariance at finite resolution.

Verification of flow towards rotationally invariant fixed points.

Abstract

In this article we extend the test of Hamiltonian Renormalisation proposed in this series of articles to the D-dimensional case using a massive free scalar field. The concepts we introduce are explicitly computed for the D=2 case but transfer immediately to higher dimensions. In this article we define and verify a criterion that monitors, at finite resolution defined by a cubic lattice, whether the flow approaches a rotationally invariant fixed point.