We study the Ward identity for the effective photon-electron vertex summing the ladder diagrams contributing to the electrical conductivity in hot QED at leading logarithmic order. It is shown that the Ward identity requires the inclusion of a new diagram in the integral equation for the vertex that has not been considered before. The real part of this diagram is subleading and therefore the final expressions for the electrical conductivity at leading logarithmic order are not affected.
We first derive the transverse Ward-Takahashi identities (WTI) of 3-dimensional quantum electrodynamics (QED$_3$) by means of the canonical quantization method and the path integration method, and then prove for the first time that QED$_3$ is strictly solvable based on the transverse WTI and the longitudinal WTI, that is, the full vector and tensor vertices functions can be expressed in term of the fermion propagators in QED$_3$. Further, we discuss the effect of different $γ$ matrix representations on the full fermion-boson vertex function. It is found that the full vector vertex function doe…
We present a general study of 3-point functions of conformal field theory (CFT) in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWIs), introduced in recent works. We investigate and detail the structure of the CWIs and their non-perturbative solutions, and compare them to perturbation theory, taking QED and QCD as examples. Exact solutions of CFT's in the flat background limit in momentum space are matched by the perturbative realizations in free field theories, showing that the origin the conformal anomaly is…
Analysis of the Phase Structure of Thermal QED/QCD through the HTL Improved Ladder Dyson-Schwinger Equation --On the Gauge Dependence of the Solution--
We present a general study of 3-point functions of conformal field theory in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWI' s), introduced in recent works by Bzowski, McFadden and Skenderis (BMS). We investigate and detail the structure of the CWI's, their non-perturbative solutions and the transition to momentum space, comparing them to perturbation theory by taking QED as an example. We then proceed with an analysis of the $TJJ$ correlator, presenting independent and detailed re-derivations of the conform…
Non perturbative studies of Schwinger-Dyson equations (SDEs) require their infnite, coupled tower to be truncated in order to reduce them to a practically solvable set. In this connection, a physically acceptable ansatz for the three point vertex is the most favorite choice. Scalar quantum electrodynamics (sQED) provides a simple and neat platform to address this problem. The most general form of the three point scalar-photon vertex can be expressed in terms of only two independent form factors, a longitudinal and a transverse one. Ball and Chiu have demonstrated that the longitudinal vertex i…
We study the semi-metal/insulator phase transition in graphene using a Schwinger-Dyson approach. We consider various forms of vertex ansaetze to truncate the hierarchy of Schwinger-Dyson equations. We define a Ball-Chiu type vertex that truncates the equations without violating gauge invariance. We show that there is a family of these vertices, parametrized by a continuous parameter that we call a, all of which satisfy the Ward identity. We have calculated the critical coupling of the phase transition using different values of a. We have also tested a common approximation in which only the fir…
