Diffeomorphisms of quantum fields

TL;DR

This paper investigates how certain transformations of quantum fields, called diffeomorphisms, affect the invariance of quantum field theories, revealing that invariance holds under specific renormalization schemes.

Contribution

It demonstrates that quantum field theories remain invariant under field diffeomorphisms only when kinematic renormalization schemes are employed.

Findings

Invariance under diffeomorphisms depends on the renormalization scheme used.

Kinematic renormalization schemes preserve the invariance.

The study applies to both free and interacting quantum fields.

Abstract

We study field diffeomorphisms $\Phi(x)= F(\rho(x))=a_0\rho(x)+a_1\rho^2(x)+\ldots=\sum_{j+0}^\infty a_j \rho^{j+1}$, for free and interacting quantum fields $\Phi$. We find that the theory is invariant under such diffeomorphisms if and only if kinematic renormalization schemes are used.