of a conformal generator $R_{\mu }$ with pure discrete spectrum. The perturbative reading of $R_{0\text{ }}$as a Hamiltonian in its own right i.e. associated with an action in a functional integral setting naturally leads to the AdS formulation. The formal service role of AdS in order to access CQFT by a standard perturbative formalism (without being forced to understand first massive theories and then taking their scale-invariant limit) vastly increases the realm of conventionally accessible 4-dim. CQFT beyond those for which one had to use Lagrangians with supersymmetry in order to have a vanishing Beta-function.'
author:
- |
    Bert Schroer\
    presently CBPF, Rua Dr. Xavier Sigaud, 22290-180 Rio de Janeiro, Brazil\
    email: schroer@cbpf.br\
    Prof. emeritus of the Institut für Theoretische Physik\
    FU-Berlin, Arnimallee 14, 14195 Berlin, Germany
date: 'May 9, 2000'
title: Particle versus Field Structure in Conformal Quantum Field Theories
---

A few introductory remarks
==========================

Ideas about the use of conformal quantum field theory entered particle physics for the first time at the height of the Kramers-Kronig dispersion relations [@Kastrup]. They were met with reactions ranging from doubts to outright rejection and the subject lay dormant for another 10 years when it reemerged on the statistical mechanics side in connection with second order phase transitions.

In the next section we will show that these early doubts of the old-time particle physicists were partially justified, because the particle structure in CQFT is indeed incompatible with interactions. However far from supplying a coffin nail for its utility in high energy physics, this no-go theorem also contains the message that one must use finer concepts in order preserve the usefulness of conformal quantum field theory as a theoretical laboratory for particle physics. There are massive particle-like objects (“infraparticles” [@Bu]) which have a continuous mass distribution with an accumulation of spectral weight at 