Radiative processes as a condensation phenomenon and the physical meaning of deformed canonical structures

Abstract

We study the radiative corrections of QED 3 from the dual point of view and show that this process is the exact dual to the Julia–Toulouse mechanism introduced by Quevedo and Trugenberger [F. Quevedo, C.A. Trugenberger, Nucl. Phys. B 501 (1997) 143] some years ago. We discuss the physics behind this mechanism that involves condensation of topological defects. It is shown that the dual Stuckelberg mechanism is responsible for the “rank-jump” phenomenon that transforms the scalar field (dual to Maxwell in this dimensionality) into the vectorial self-dual field. This phenomenon is studied using the ideas of noncommutative fields theory that examines possible deformations of the canonical structure of some well-known models in ( 2 + 1 ) D . A deformation is constructed linking the massless scalar field theory with the self-dual theory. This is the exact dual of the known deformation connecting the Maxwell theory with the Maxwell–Chern–Simons theory. Duality, radiative corrections, the Julia–Toulouse mechanism and canonical deformations are then used to establish a web of relations between the mentioned theories and to propose a physical picture of the deformation procedure adopted.