Dynamical breakdown of chirality and parity in (2+1)-dimensional QED

Abstract

In the (2+1)-dimensional QED with and without the Chern-Simons term, we find the non-local gauge in which there is no wavefunction renormalization for the fermion in the framework of the Schwinger-Dyson equation. By solving the Schwinger-Dyson equation in the non-local gauge, we find a finite critical value N c f for the number of flavors N f of four-component Dirac fermions, above which the chiral symmetry restores irrespective of presence or absence of the Chern-Simons term. In the same framework, we study the possibility of dynamical breakdown of the parity. It is shown that the parity is not dynamically broken. We discuss this reason from the viewpoint of the Schwinger-Dyson equation. *

Thirring model as a gauge theory

“…In the SD equation approach, it has been confirmed [20,40] that neglecting higher powers of the series in k/α does not change the qualitative feature of the chiral phase transition (infrared dominance).…”

Dynamical Mass Generation in QED3 with Chern-Simons Term

“…We used both the Landau gauge and a nonlocal gauge 7 ) to keep A± c::= 1. In Landau gauge, A± will in general not be equal to one, but we nevertheless set it equal to one, in order to be consistent with the bare vertex approximation.…”

“…4 ), s) The CS term generates a parity-odd mass term for the fermions, but in addition there might be a parity-even mass, which breaks chirality. 6 ), 7 ) Both numerical and analytical studies of the truncated Dyson-Schwinger (DS) equation for the fermion propagator show that there is a first-order phase transition. 4 ) This is quite remarkable and in contrast to the infinite-order phase transition one finds in pure QED3.…”

Determine the critical fermion flavor in three-dimensional QED using nonlocal gauge

“…At finite temperature QED 3 , there still exists a critical fermion flavor, which will be reduced by the temperature increasing. [24][25][26][27][28] In the nonlocal gauge, [9][10][11][29][30][31][32][33] the gauge parameter ξ is dependent on the momentum or coordinates, while in the usual R ξ gauge, ξ is just a constant. The nonlocal gauge can be transformed into the Landau gauge by the inverse LKFT.…”

“…In the vicinity of the critical point, these equations are decoupled and we need only to deal the integral equation of mass function B. For the simple polarization of single massless fermion loop and the vertex proportional to the bare one, Kondo et al [9][10][11] gave the result N c = 128/3π 2 . The validity of the nonlocal gauge method has been exemplified 33 in the study of the IR behavior of the running coupling constant and the nontrivial IR fixed point in QED 3 .…”