Not too little intervals for quantum mechanics

TL;DR

This paper presents a discrete model for the free scalar field on the real line, extending a general framework to a one-dimensional example and adapting existing methods to a discrete setting.

Contribution

It introduces a discrete model for the free scalar field in one dimension, building on previous frameworks and adapting them to a new setting.

Findings

Demonstrates a discrete scalar field model on the real line.

Adapts Costello--Gwilliam's treatment to a discrete context.

Extends the framework from 'Not too little discs' to a 1D example.

Abstract

This short paper illustrates the general framework introduced in the paper "Not too little discs" (arXiv:2407.18192), joint with Victor Carmona, on yet another one dimensional example. It exhibits a discrete model for the free scalar field on the real line, adapting the treatment from the book of Costello--Gwilliam to the discrete setting.