Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-05-12
Phys.Lett. B494 (2000) 124-129
Physics
High Energy Physics
High Energy Physics - Theory
9 pages tcilatex, reference added, some typos corrected
Scientific paper
10.1016/S0370-2693(00)01103-5
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 $R_{0\text{}}$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.
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