Renormalisation in Open Quantum Field theory II: Yukawa theory and PV reduction

TL;DR

This paper advances the understanding of open quantum field theories by computing PV reduction for tensor integrals, applying it to Yukawa theory, and revealing persistent non-local divergences in one-loop fermionic self-energy corrections.

Contribution

It introduces PV reduction techniques for open quantum field theories and demonstrates their application to Yukawa theory, highlighting non-local divergences in loop corrections.

Findings

Non-local divergences appear in one-loop fermionic self-energy.

PV reduction is applicable to open quantum field theories.

Non-local divergences persist despite trace-preserving conditions.

Abstract

We compute Passarino-Veltman (PV) reduction for tensor loop integrals, that appear in open field theories. We apply these results to open-Yukawa theory and compute the self-energy correction of the fields. We found that non-local divergences show up in the one loop correction to the fermionic self-energy. These non-local divergences do not disappear even if the tree level theory is chosen to satisfy the trace preserving condition of the density matrix.