Gauge-covariant solution for the Schwinger-Dyson equation in 3D QED with a Chern-Simons term

Abstract

An Abelian gauge theory with Chern-Simons (CS) term is investigated for a fourcomponent Dirac fermion in 1+2 dimensions. The Ball-Chiu (BC) vertex function is employed to modify the rainbow-ladder approximation for the Schwinger-Dyson (SD) equation. We numerically solve the SD equation and show the gauge dependence for the resulting phase boundary for the parity and the chiral symmetry.

New point-like sources and a conducting surface in Maxwell–Chern–Simons electrodynamics

“…(23) is an effect due solely to Maxwell-Chern-Simons electrodynamics, because if we take the limit m → 0 there is no interaction energy. On the contrary to the energy (15), which is non-vanishing for m = 0, as we can see in (18).…”

“…In order to verify this fact we must take the limit m → 0 in Eq. (15). In this case, all terms which depend on V 0 or U 0 vanishes, and we are taken to the same interaction obtained for two electric dipoles (12), namely…”

“…One of the most important class of models of this kind is the so called Maxwell-Chern-Simons electrodynamics [2], or Abelian topological massive gauge theory [3], which is relevant because it is simultaneously massive and gauge invariant. Theoretical aspects of Maxwell-Chern-Simons electrodynamics have been investigated in Casimir effect [4][5][6][7][8][9], quantum dissipation of harmonic systems [10], quantum electrodynamics (QED 3 ) [11][12][13][14][15], dynamical mass generation [16,17], condensed matter physics (see, for instance, Ref. [18] and references therein), description of graphene properties [19][20][21][22][23][24], noncommutativity [25][26][27][28], strings theory [29], dynamics of vortices [30,31], and with a planar boundary [32][33][34][35][36], to mention just a few.…”

Phase Transition in Topologically Massive QED

“…Recently we obtained the numerical solutions with this approximation [6], [7].It is said that the vortex destroys condensate in condensed matter physics.At bare vertex or inclusion the BC vertex we find µ cr ≃ 0.01e 2 which is the same order of magnitude with Raya et.al [6] …”

“…QED 3 with Chern-Simons term has a vortex solution for vector potential by solving Maxwell equation with charged particle [4]. Therefore the situation is similar to the isolated vortex inside superfluid at high temperature.We can examine the phase transition by solving Dyson-Schwinger equation for the fermion selfenergy for chiral condensate and its destruction by vortices.In this model Chern-Simons term is absorbed to parity odd part of the gauge boson propagator and gauge boson acquires a mass.Pure QED part of gauge boson contributes to the condensation of ee,while the latter may wash away the condensate at zero temperature.These are the main goals of our analysises.In 4-dimensional representation of spinor we have chiral symmetry for massless fermion.If it breaks dynamically we have two kinds of mass as chiral symmetry breaking and parity violation.For infinitesimal value of the topological mass it has been pointed out by K.I.Kondo and P.Maris that chiral symmetry restores and parity violating phase remains within 1/N expansion and nonlocal gauge of Dyson-Schwinger equation [5], [6], [7].Here we consider weak coupling and gauge covariant approximation which satisfy Ward-Takahashi relation at first.After that we examine the 1/N expansion in the Landau gauge.In the final section we evaluate the spectral function of the fermion propagator [8], [9] .This method is helpful to determine the infrared behaviour or one particle singularity of the propagator in the existence of massless boson as photon,which has been known in QED 3+1 .Since QED 2+1 is super renormalizable we get a short distance behaviour of the fermion propagator too.As a result we show the effect of vortex on the lowest order spectral function of parity even scalar part of the propagator.So that we find the critical value of topological mass above which chiral condensate is washed away. Fortunately this value coincides with that obtained by numerical analysis of Dyson-Schwinger equations.…”