Dynamical mass generation in three-dimensional QED: Improved vertex function

Critical behavior of (2+1)-dimensional QED:1/Nfcorrections in the Landau gauge

“…On the other hand, in a more refined analysis of the gap equation at LO of the 1/N -expansion, Appelquist et al 2 have shown that the theory exhibits a critical behaviour as the number N of fermion flavours approaches N c = 32/π 2 ; that is, a fermion mass is dynamically generated only for N < N c . Contrary to all previous results, an alternative non-perturbative study by Atkinson et al 5 suggested that chiral symmetry is unbroken at sufficiently large N . The theory has also been simulated on the lattice.…”

“…Originally, the interest in QED 3 came from its similarities to (3 + 1)-dimensional QCD and the fact that phenomena such as dynamical chiral symmetry breaking (DχSB) and mass generation may be studied systematically in such a toy model, see, e.g., Refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Later, a strong interest in QED 3 arose in connexion with planar condensed matter physics systems having relativistic-like low-energy excitations such as some two-dimensional antiferromagnets 17 and graphene; 18 the study of a dynamically generated gap in the fermion spectrum of graphene has now become an active area of research, see, e.g., the reviews Refs.…”

Critical behavior of (2+1)-dimensional QED:1/Nfcorrections in an arbitrary nonlocal gauge

“…An accurate determination of N c is of crucial importance to understand the phase structure of QED 3 with far reaching implications from particle physics to planar condensed matter physics systems having relativistic-like low-energy excitations such as some two-dimensional antiferromagnets [23] and graphene [24]. It turns out that the values that can be found in the literature vary from N c → ∞ [3,[5][6][7] corresponding to DχSB for all values of N , all the way to N c → 0 in the case where no sign of DχSB is found [8,9]. Recent works based on conformal field theory techniques tend to narrow this range but the upper bound found for N c still varies: N c < 3/2 [10] or N c < 4.4 [11] or N c < 9/4 [12].…”

“…Early studies of this model [3,4] suggested that the physics is rapidly damped at momentum scales p a and that a (parity-invariant) fermion mass term breaking the flavour symmetry is dynamically generated at scales which are orders of magnitude smaller than the intrinsic scale a. Since then, dynamical chiral symmetry breaking (DχSB) in QED 3 and the dependence of the dynamical fermion mass on N have been the subject of extensive studies, see, e.g., [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

How gauge covariance of the fermion and boson propagators in QED constrain the effective fermion-boson vertex

“…Solutions in the Minkowski space have been obtained by [32] (also see Ref. [33][34][35][36][37]). Alternatively, these equations can be solved using complex conjugate poles to represent the propagator functions [5,[38][39][40].…”