Short-Distance Behavior of agφ4Theory, and Conformal-Invariant Four-Point Functions

Abstract

The "zero-mass" limiting short-distance theory for the $g{\phi }^4$ interaction is explicitly constructed. The propagator is computed to third order and the vertex to fourth order in $g$, the zero-mass coupling constant. The Gell-Mann and Low short-distance equations which result as exact consequences can be explicitly determined to all orders in perturbation theory. If the eigenvalue condition is imposed, one can construct a theory in terms of the massless free propagator and a conformal-invariant four-point vertex function only. The energy-momentum tensor of this theory is the same as that proposed by Callan, Coleman, and Jackiw.