Operator regularization and multiloop Green's functions

Abstract

We present in this paper the evaluation of multiloop Green's functions in the context of a recently proposed regulating scheme called operator regularization. We show that, in contrast with other schemes, imposing the requirement of unitarity (rather than finiteness) is crucial in obtaining the (perturbative) renormalized effective action and Green's functions of a given theory. We demonstrate how an evaluation of these quantities may be carried out using this regulating technique in a manner which preserves the unitarity of the S matrix. This method is then applied to a two-loop calculation in the (44)4 theory, yielding agreement with results obtained in other schemes. Specifically, we calculate the B function, y , function, and the anomalous dimension of the field without having to look at the relationship between bare and renormalized quantities. Indeed, they directly come from the finite sector of the Green's functions.

Structure of the effective potential in nonrelativistic Chern-Simons field theory

“…We use 1) operator regularization (OR) [10,11] and 2) the cutoff regularization method. The first method was proposed a few years ago and regularizes the operators present in the theory instead of modifying the original Lagrangian by either adding counterterms or massive fields.…”

Proper-time regularization and topological mass ambiguity in three-dimensional QCD

“…In particular, we have shown that proper-time regularization yields a result in agreement with analytic [6], dimensional [7], operator [8], and nonlocal [9] regularizations, and in disagreement with Pauli-Villars [4] regularization. Nevertheless, we may also reproduce in this context the result of the Pauli-Villars regularization by introducing a Pauli-Villars cutoff in (3.6) as…”

“…In the limit m -m , rIF) vanishes as This is to be contrasted with the result obtained via analytic [6], dimensional [7], operator [8], and nonlocal [9] regularizations, which yield a CS term surviving in this limit:…”

“…[6-91, different gauge-invariant regularization procedures yield different results for the CS term. As a consequence one finds that in analytic [6], dimensional [7], operator [8], and nonlocal [9] regularization schemes this radiatively generated CS term induces a mass for the gauge field A,, whereas A, remains massless in the case of Pauli-Villars regularization.…”

“…Since in a gauge-invariant regularization scheme this CS term turns out to be ultraviolet (UV) finite, one might expect for any such scheme an unambiguous, unique result. It nevertheless turns out that at least a twofold ambiguity exists, having direct physical implications: while in a Pauli-Villars (PV) regularization scheme the (originally massless) gauge boson remains massless, this is not the case in analytic [6], dimensional [7], operator [8], and nonlocal [9] regularization schemes. It is therefore of interest to examine this problem in the context of one further regularization scheme-that of proper-time [lo] (or < function) regularization.…”