Gauge invariant cutoff QED

Abstract

A hidden generalized gauge symmetry of a cutoff QED is used to show the renormalizability of QED. In particular, it is shown that corresponding Ward identities are valid all along the renormalization group flow. The exact Renormalization Group flow equation corresponding to the effective action of a cutoff λϕ 4 theory is also derived. Generalization to any gauge group is indicated.

Cutoff function in holographic RG flow

“…There is an alternative method of imposition of cutoff on the momentum modes which will be natural for the precursor map considerations. In this scheme, the momentum space fields are directly multiplied by a cutoff function, so that the higher-momentum modes are "almost deemphasized" in the fields, to begin with [10],…”

“…There is an RG scheme, though, in which the correspondence between the two cutoff functions is straightforward [10]. In this scheme, the momentum cutoff is directly im-posed on the fields themselves via multiplication of the fields by a cutoff function in the momentum space.…”

Green’s functions for translation invariant star products

“…Here we are mainly interested in the noncommutative products, which give rise to the commutator (1.1). See however [10,14] where a non-local commutative product has been suggested as an alternative tool for regularization of UV divergences.…”

“…the case of a commutative non local product, there is only a correction of the kind e − aη (ka) . This term could be used as a regulator, along the lines of [10,14].…”

Commutative deformations of general relativity: nonlocality, causality, and dark matter

“…Here we apply Hopf algebras to commutatively deformed curved classical manifolds, where f g = g f . The commua e-mail: Paul.deVegvar@post.harvard.edu tative deformation approach to classical manifolds has just recently begun to be explored by researchers [7][8][9] who studied flat spacetime. In this work the Hopf algebra approach is physically motivated by recent studies [10] about how background independent theories of canonical quantum gravity can display microcausality in some suitable classical limit; that is, explaining how gauge invariant operators (Dirac observables) at spacelike distances can commute in generically curved spacetimes.…”