Dynamical Masses and Confinement in QED 3

Nuclear Physics B, 2005

Numerical study of the Schwinger-Dyson equation (SDE) for the fermion propagator (FP) to obtain dynamically generated chirally asymmetric solution in an arbitrary covariant gauge ξ is a complicated exercise specially if one employs a sophisticated form of the fermion-boson interaction complying with the key features of a gauge field theory. However, constraints of gauge invariance can help construct such a solution without having the need to solve the Schwinger-Dyson equation for every value of ξ . In this article, we propose and implement a method to carry out this task in quenched quantum electrodynamics in a plane (QED3). We start from an approximate analytical form of the solution of the SDE for the FP in the Landau gauge. We consider the cases in which the interaction vertex (i) is bare and (ii) is full. We then apply the Landau-Khalatnikov-Fradkin transformations (LKFT) on the dynamically generated solution and find analytical results for arbitrary value of ξ . We also compare our results with exact numerical solutions available for a small number of values of ξ obtained through a direct analysis of the corresponding SDE.

… and Fields: Proceedings of the XIII …, 2009

We study the gauge invariance of physical observables related to confinement and dynamical chiral symmetry breaking in unquenched QED3 for a simple truncation of the corresponding Schwinger-Dyson equations in arbitrary covariant gauges. An explicit implementation of Landau-Khalatnikov-Fradkin transformations renders these observables gauge independent.

Numerical study of the Schwinger-Dyson equation (SDE) for the fermion propagator (FP) to obtain dynamically generated chirally asymmetric solution in an arbitrary covariant gauge ξ is a complicated exercise specially if one employs a sophisticated form of the fermion-boson interaction complying with the key features of a gauge field theory. However, constraints of gauge invariance can help construct such a solution without having the need to solve the Schwinger-Dyson equation for every value of ξ . In this article, we propose and implement a method to carry out this task in quenched quantum electrodynamics in a plane (QED3). We start from an approximate analytical form of the solution of the SDE for the FP in the Landau gauge. We consider the cases in which the interaction vertex (i) is bare and (ii) is full. We then apply the Landau-Khalatnikov-Fradkin transformations (LKFT) on the dynamically generated solution and find analytical results for arbitrary value of ξ . We also compare our results with exact numerical solutions available for a small number of values of ξ obtained through a direct analysis of the corresponding SDE.

A nonperturbative construction of the 3-point fermion-boson vertex which obeys its Ward-Takahashi or Slavnov-Taylor identity, ensures the massless fermion and boson propagators transform according to their local gauge covariance relations, reproduces perturbation theory in the weak coupling regime and provides a gauge independent description for dynamical chiral symmetry breaking and confinement has been a long-standing goal in physically relevant gauge theories such as quantum electrodynamics (QED) and quantum chromodynamics. In this paper, we demonstrate that the same simple and practical form of the vertex can achieve these objectives not only in 4-dimensional quenched QED but also in its 3-dimensional counterpart. Employing this convenient form of the vertex ansatz into the Schwinger-Dyson equation for the fermion propagator, we observe that it renders the critical coupling in 4-dimensional quenched QED markedly gauge independent in contrast with the bare vertex and improves on the well-known Curtis-Pennington construction. Furthermore, our proposal yields gauge independent order parameters for confinement and dynamical chiral symmetry breaking in 3-dimensional quenched QED.

We study the Landau-Khalatnikov-Fradkin transformations (LKFT) in momentum space for the dynamically generated mass function in QED3. Starting from the Landau gauge results in the rainbow approximation, we construct solutions in other covariant gauges. We confirm that the chiral condensate is gauge invariant as the structure of the LKFT predicts. We also check that the gauge dependence of the constituent fermion mass is considerably reduced as compared to the one obtained directly by solving SDE.

are an ideal framework to study non-perturbative phenomena such as dynamical chiral symmetry breaking (DCSB). A reliable truncation of these equations leading to gauge invariant results is a challenging problem. Constraints imposed by Landau-Khalatnikov-Fradkin transformations (LKFT) can play an important role in the hunt for physically acceptable truncations. We present these constrains in the context of dynamical mass generation in QED in 2 + 1-dimensions.

Annals of Physics, 2012

We study chiral symmetry breaking in QCD-like gauge theories introducing a confining effective propagator, as proposed recently by Cornwall, and considering the effect of dynamical gauge boson mass generation. The effective confining propagator has the form 1/(k 2 + m 2) 2 and we study the bifurcation equation finding limits on the parameter m below which a satisfactory fermion mass solution is generated. Considering the evidences that the coupling constant and the gauge boson propagator are damped in the infrared, due to the presence of dynamically massive gauge bosons, the major part of the chiral breaking is mostly due to the confining propagator. We study the asymptotic behavior of the gap equation containing confinement and massive gauge boson exchange, and find that the symmetry breaking can be approximated at some extent by an effective four-fermion interaction generated by the confining propagator. We compute some QCD chiral parameters as a function of m, finding values compatible with the experimental data. Within this approach we expect that lattice simulations should not see large differences between the confinement and chiral symmetry breaking scales independent of the fermionic representation and we find a simple approximate relation between the fermion condensate and dynamical mass for a given representation as a function of the parameters appearing in the effective confining propagator.

Physical Review C, 2008

We establish that QED3 can possess a critical number of flavours, N c f , associated with dynamical chiral symmetry breaking if, and only if, the fermion wave function renormalisation and photon vacuum polarisation are homogeneous functions at infrared momenta when the fermion mass function vanishes. The Ward identity entails that the fermion-photon vertex possesses the same property and ensures a simple relationship between the homogeneity degrees of each of these functions. Simple models for the photon vacuum polarisation and fermion-photon vertex are used to illustrate these observations. The existence and value of N c f are contingent upon the precise form of the vertex but any discussion of gauge dependence is moot. We introduce an order parameter for confinement. Chiral symmetry restoration and deconfinement are coincident owing to an abrupt change in the analytic properties of the fermion propagator when a nonzero scalar self-energy becomes insupportable.

The ambiguities associated with the lack of gauge invariance in the non-perturbative truncations of Schwinger-Dyson equations (SDEs) are a challenging problem which has not yet been resolved in a decisive fashion. Pursuing this aim, we study dynamical chiral symmetry breaking in quantum electrodynamics in three space-time dimensions (QED3). We investigate the gauge dependence of the chiral condensate both in the quenched and the unquenched versions of the theory and emphasize the importance of taking into account the gauge covariance properties of the fermion propagator as dictated by its Landau-Khalatnikov-Fradkin transformation (LKFT). We present numerical solutions of the SDE of the fermion propagator which respect Ward-Green-Takahashi identities (WGTI) and LKFT simultaneously. As a striking consequence, we obtain a practically gauge independent chiral condensate.

are an ideal framework to study nonperturbative phenomena such as dynamical chiral symmetry breaking (DCSB). Loss of gauge invariance is an obstacle to achieve fully reliable predictions from these equations. In addition to Ward-Green-Takahashi identity (WGTI), Landau-Khalatnikov-Fradkin transformations (LKFT) also play an important role in restoring the said invariance at the level of physical observables. On one hand, they impose useful constraints on the transverse part of the fermion-boson vertex and on the other, they govern the change in dynamically generated fermion propagator with a variation of gauge. We consider the latter in this article and study the gauge (in)dependence of chiral condensate in quantum electrodynamics in (2+1) space-time dimensions (QED3). 1 One should keep in mind that planar field theories display unusual properties such as having arbitrary spin and statistics and peculiar parity and chiral transformations, see for example .