On the critical behavior of (2 + 1)-dimensional QED
- PDF / 396,694 Bytes
- 3 Pages / 612 x 792 pts (letter) Page_size
- 88 Downloads / 149 Views
ELEMENTARY PARTICLES AND FIELDS Theory
On the Critical Behavior of (22 + 11)-Dimensional QED* A. V. Kotikov** Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, Russia Received March 31, 2011
Abstract—It is shown the analysis [1] for QED in (2 + 1) dimensions with N four-component fermions in the leading and next-to-leading orders of the 1/N expansion. As it was demonstrated in [1], the range of the admissible values N , where the dynamical fermion mass exists, decreases strongly with the increasing of the gauge charge. So, in Landau gauge the dynamical chiral symmetry breaking appears for N < 3.78, that is very close to the results of the leading order and in Feynman gauge dynamical mass is completely absent. DOI: 10.1134/S1063778812070058
Quantum Electrodynamics in (2 + 1) dimensions (QED3 ) has acquired increasing attention [1–7] because of its similarities to (3 + 1)-dimensional QCD. Moreover, last years a new strong interest comes to QED3 in the relation with graphene properties (see [8] and discussions and references therein). Graphene, a one-atom-thick layer of graphite, is a remarkable system with many unusual properties that was fabricated for the first five years ago [9]. Theoretically it was shown long ago [10] that quasiparticle excitations in graphene are described by the massless Dirac equation in (2 + 1) dimension. This explains why the bilayer graphene in external fields is a subject of intensive recent study [11]. A number of investigations have been performed for the study of dynamical chiral symmetry breaking in QED3 and very different results have been obtained. Using the leading order (LO) in the 1/N expansion of the Schwinger–Dyson (SD) equation, Appelquist et al. [2] showed that the theory exhibits a critical behavior as the number N of fermion flavor approaches Nc = 32/π 2 ; that is, a fermion mass is dynamically generated only for N < Nc . On the contrary, Pennington and collaborators [3], adopting a more general non-perturbative approach to the SD equations, found that the dynamically generated fermion mass decreases exponentially with N , vanishing only as N → ∞. This conclusion was supported also by Pisarski [4] by the use of the other methods. On the other hand, an alternative nonperturbative study by Atkinson et al. [5] suggested that chiral symmetry is unbroken at sufficiently large ∗ **
The text was submitted by the author in English. E-mail: [email protected]
N . The theory has also been simulated on the lattice [6, 7]. Remarkably, the conclusions of [6] are in agreement with the existence of a critical N as predicted in the analysis of [2], while the second paper [7] contains the opposite results. Because the critical value Nc is not large, the contribution of the higher orders in the 1/N expansion can be essential and may lead to better understanding of the problem. The purpose of this work is to consider the 1/N correction [1, 12] to LO result [2]. 1. The Lagrangian of massless QED3 with N flavors is 2 ¯ ∂ˆ − eA)Ψ ˆ − 1 Fμν , L = Ψ(i 4 where Ψ is taken to be a four-compone
Data Loading...
