Loop quantization as a continuum limit

TL;DR

This paper develops a continuum limit approach for loop quantized theories using Wilson's renormalization group, demonstrated through the example of the 2d Ising field theory, an interacting quantum field model.

Contribution

It introduces a novel continuum limit formalism for loop quantization, enabling the construction of dynamics from effective theories, exemplified by the 2d Ising model.

Findings

Successful implementation of continuum limit for loop quantization

Application to 2d Ising field theory as a proof of concept

Establishment of a framework for loop quantized interacting theories

Abstract

We present an implementation of Wilson's renormalization group and a continuum limit tailored for loop quantization. The dynamics of loop quantized theories is constructed as a continuum limit of dynamics of effective theories. After presenting the general formalism we show as first explicit example the 2d Ising field theory. It is an interacting relativistic quantum field theory with local degrees of freedom quantized by loop quantization techniques.