Algebraic renormalization of parity-preserving QED3 coupled to scalar matter II: broken case

Abstract

In this letter the algebraic renormalization method, which is independent of any kind of regularization scheme, is presented for the parity-preserving QED 3 coupled to scalar matter in the symmetric regime, where the scalar assumes vanishing vacuum expectation value, ϕ =0. The model shows to be stable under radiative corrections and anomaly free.The study of gauge field theories in 3 space-time dimensions [1] has been well-supported by a possible field-theoretical approach to describe some Condensed Matter phenomena, such as High-T c Superconductivity and Quantum Hall Effect [2,3]. Some Abelian models have been proposed in this direction, namely, the QED 3 and τ 3 QED 3 [4,5].One of the interesting properties of 3-dimensional gauge field theories is the Landau gauge finiteness of non-Abelian Chern-Simons theories [6].The confinement of massive electrons in 3 space-time dimensions is a remarkable characteristic of this lower dimensional space [7]. Recently, it was shown by using the Bethe-Salpeter equations that in a parity-preserving QED 3 there are bound states in electron-positron systems, positronium states [8].In a recent work [9], a parity-preserving QED 3 with spontaneous breaking of a local U(1)-symmetry was proposed. The breakingdown is accomplished by a sixth-power potential. It was shown that electrons scattered in D=1+2 can experience a mutual attractive interaction, depending on their spin states, where the intermediate bosons involved in *

ELECTRON–ELECTRON ATTRACTIVE INTERACTION IN MAXWELL–CHERN–SIMONS QED3 AT ZERO TEMPERATURE

“…where the V (ϕ * ϕ) is a sixth-power potential, being the most general renormalizable U (1)-invariant potential in three dimensions [9,10]:…”

“…In the latest years, planar QED (QED 3 ) [1][2][3][4][5][6][7][8][9][10][11] has been object of intensive investigation, both by its formal aspects and by the possibilities of application to important phenomena in the realm of Condensed Matter Physics, namely high-T c superconductivity and quantum Hall effect. The first phenomenon, as well-known, is related to the existence of electron-electron bound states, but the nature of these pairs belonging to high-T c phase is not still set up.…”

“…Similarly, in Refs. [9,10], the Higgs mechanism has been used in the framework of a paritypreserving QED 3 in searching for electron-electron bound states. The symmetry breaking is accomplished by a sixth-power potential, where a Higgs scalar and a massive gauge boson (Maxwell-Chern-Simons-Proca) stem as a by-product from the breaking of a local U (1)-symmetry.…”

Electron-electron bound states in Maxwell-Chern-Simons-Proca QED $\scriptstyle \mathsf {}$ 3

“…which is responsible for the SSB; it is the most general one renormalizable in 1 + 2 dimensions [13]. The mass dimensions of the parameters µ, ζ, λ and y are respectively: 1,1,0 and 0.…”

Algebraic renormalization of parity-preserving QED3 coupled to scalar matter I: unbroken case

“…Rigid invariance itself follows from the antighost equation (7.c) and from the validity of the Slavnov-Taylor identity(10).…”