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 $R_{\mu }$ with pure discrete spectrum. The perturbative reading of $R_0$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.

9 pages tcilatex, reference added, some typos corrected

References in corpus (6)

• Algebraic Holography
• Polarization-Free Generators and the S-Matrix
• Non-renormalization of next-to-extremal correlators in N=4 SYM and the AdS/CFT correspondence
• Local Quantum Observables in the Anti-deSitter - Conformal QFT Correspondence
• Aspects of the conformal operator product expansion in AdS/CFT correspondence
• Facts and Fictions about Anti deSitter Spacetimes with Local Qantum Matter

Cited by in corpus (5)

• Pascual Jordan, his contributions to quantum mechanics and his legacy in contemporary local quantum physics
• Braided Structure in 4-dimensional conformal Quantum Field Theory
• Causality and dispersion relations and the role of the S-matrix in the ongoing research
• The paradigm of the area law and the structure of transversal and longitudinal lightfront degrees of freedom
• Anomalous Scale Dimensions from Timelike Braiding