Physics Fun with Discrete Scale Invariance

TL;DR

This paper introduces a quantum field theory model exhibiting discrete scale invariance, exploring its mathematical properties and potential physical implications beyond standard effective field theory concepts.

Contribution

It constructs a novel quantum field theory with discrete scale invariance and investigates its unique mathematical features and possible physical significance.

Findings

Model exhibits discrete scale invariance at tree level

Mathematical properties include q-hypergeometric series

Potential physical implications beyond standard effective theories

Abstract

I construct a quantum field theory model with discrete scale invariance at tree level. The model has some unusual mathematical properties (such as the appearance of $q$-hypergeometric series) and may possibly have some interesting physical properties as well. In this note, I explore some possible physics that could be regarded as a violation of standard effective field theory ideas.