Vacuum Radiation and Symmetry Breaking in Conformally Invariant Quantum Field Theory

TL;DR

This paper explores the reasons behind the challenges in implementing the full conformal group in massless quantum field theories, revealing a fundamental symmetry breakdown and analyzing vacuum radiation under special conformal transformations.

Contribution

It demonstrates the dynamical breakdown of conformal symmetry in massless QFT and provides an exact calculation of the vacuum radiation spectrum under special conformal transformations.

Findings

The special conformal subgroup action causes symmetry breakdown.

Vacuum radiates with a generalized Planckian spectrum.

The spectrum reduces to Planckian in a specific limit.

Abstract

The underlying reasons for the difficulty of unitarily implementing the whole conformal group $SO(4,2)$ in a massless Quantum Field Theory (QFT) are investigated in this paper. Firstly, we demonstrate that the singular action of the subgroup of special conformal transformations (SCT), on the standard Minkowski space $M$, cannot be primarily associated with the vacuum radiation problems, the reason being more profound and related to the dynamical breakdown of part of the conformal symmetry (the SCT subgroup, to be more precise) when representations of null mass are selected inside the representations of the whole conformal group. Then we show how the vacuum of the massless QFT radiates under the action of SCT (usually interpreted as transitions to a uniformly accelerated frame) and we calculate exactly the spectrum of the outgoing particles, which proves to be a generalization of the Planckian one, this recovered as a given limit.