Particle versus field structure in conformal quantum field theories

Abstract

I show that a particle structure in conformal field theory is incompatible with interactions. As a substitute one has particle-like exitations whose interpolating fields have in addition to their canonical dimension an anomalous contribution. The spectra of anomalous dimension is given in terms of the Lorentz invariant quadratic invariant (compact mass operator) of a conformal generator Rµ with pure discrete spectrum. The perturbative reading of R0 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. A few introductory remarksIdeas about the use of conformal quantum field theory entered particle physics for the first time at the height of the Kramers-Kronig dispersion relations [1]. 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.

Anomalous scale dimensions from time-like braiding

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String Theory, the Crisis in Particle Physics and the Ascent of Metaphoric Arguments

“…This was put on solid mathematical grounds in [72] where it also argued that, since the scale invariance demands that all multiparticle threshholds fall on top of each other, one should expect that information on highly inclusive processes is retained. The still open problem is whether the inclusiveness demands the summation over only infinitely many outgoing configurations or if also an averaging over incoming ones is required.…”

Facts and Fictions About Anti deSitter Spacetimes¶with Local Quantum Matter

“…The present analysis of the AdS-CQFT correspondence has its roots in the LSZ setting of particle physics from which the conformally invariant QFT should result in the zero mass limit [30]. The step from the traditional use of pointlike (Lagrangian) fields to operator algebras indexed by spacetime regions has been taken a long time ago with the intention to obtain a more profound understanding of the observed insensitivity of the S-matrix obtained as the asymptotic limit in the setting of the Lehmann Symanzik-Zimmermann formalism to changes of field coordinates ("interpolating fields") within the (Borchers) equivalence class.…”