Related papers: Renormalization of composite operators
We extend the OPE-based renormalization algorithm to composite operators with operator mixing, focusing on scalar operators in $\phi^4$ and $\phi^3$ models. Using the OPE of operators with a fundamental field, we show that the $Z$-factors…
The blocking step of the renormalization group method is usually carried out by restricting it to fluctuations and to local blocked action. The tree-level, bi-local saddle point contribution to the blocking, defined by the infinitesimal…
The renormalization of the periodic potential is investigated in the framework of the Euclidean one-component scalar field theory by means of the differential RG approach. Some known results about the sine-Gordon model are recovered in an…
We consider the multiple products of relevant and marginal scalar composite operators at the Gaussian fixed-point in $D=4$ dimensions. This amounts to perturbative construction of the $\phi^4$ theory where the parameters of the theory are…
Using on-shell methods, we present a new perturbative non-renormalization theorem for operator mixing in massless four-dimensional quantum field theories. By examining how unitarity cuts of form factors encode anomalous dimensions we show…
In this paper we study systematically the Euclidean renormalization in configuration spaces. We investigate also the deviation from commutativity of the renormalization and the action of all linear partial differential operators. This…
We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space…
We study perturbative renormalization of the composite operators in the $T\bar T$-deformed two-dimensional free field theories. The pattern of renormalization for the stress-energy tensor is different in the massive and massless cases.…
The partial success of the block renormalization group techniques is analysed in terms of a functional operator which formalizes the idea of self-replicability of a system in terms of smaller blocks which are similar to the original. The…
In QCD sum-rule methods, the fundamental field-theoretical quantities are correlation functions of composite operators that serve as hadronic interpolating fields. One of the challenges of loop corrections to QCD correlation functions in…
For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…
Essential to QCD applications of the operator product expansion, etc., is a knowledge of those operators that mix with gauge-invariant operators. A standard theorem asserts that the renormalization matrix is triangular: Gauge-invariant…
We study the dynamics of the renormalization operator for multimodal maps. In particular, we prove the exponential convergence of this operator for infinitely renormalizable maps with same bounded combinatorial type.
We consider defect operators in scalar field theories in dimensions $d=4-\epsilon $ and $d=6-\epsilon$ with self-interactions given by a general marginal potential. In a double scaling limit, where the bulk couplings go to zero and the…
We consider a recursive scheme for defining the coefficients in the operator product expansion (OPE) of an arbitrary number of composite operators in the context of perturbative, Euclidean quantum field theory in four dimensions. Our…
Given a renormalizable theory we construct the dilatation operator, in the sense of generator of RG flow of composite operators. The generator is found as a differential operator acting on the space of normal symbols of composite operators…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded perturbation is considered. The objective is to estimate the norm of the difference of two spectral projections associated with isolated parts…
We study the effective potential for composite operators. Introducing a source coupled to the composite operator, we define the effective potential by a Legendre transformation. We find that in three or fewer dimensions, one can use the…
We derive a set of rotationally covariant amplitude equations for use in multiscale simulation of the two dimensional phase field crystal (PFC) model by a variety of renormalization group (RG) methods. We show that the presence of a…
We prove that the real four-dimensional Euclidean noncommutative \phi^4-model is renormalisable to all orders in perturbation theory. Compared with the commutative case, the bare action of relevant and marginal couplings contains…