One loop expressions for fermion self energy,vacuum polarization and vertex correction in light front time ordered perturbation theory (LFTPOT) can be obtained from respective covariant expressions by performing k^- integration. In earlier work, we have shown that the third term in the doubly transverse gauge propagator is necessary to generate the diagrams involving instantaneous photon exchange both in case of fermion self-energy as well as vertex correction.In this work,we show that instantaneous photon exchange diagrams in fermion self-energy as well as th IR singular terms in the propagating diagrams can be generated by taking the asymptotic limit of the covariant expression,if one uses the commonly used two term photon propagator.We also show that this method reproduces the IR singular terms in propagating diagrams of vacuum polarization.
In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green's functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists i…
We revisit the proof of equivalence of one loop expressions for fermion self-energy and vertex correction in light-front QED and Covariant QED at the Feynman diagram level and generalize, to all components, the proof of equivalence for the one loop vertex correction diagram which was presented earlier by us only for the $+$ component of $Λ^μ$. We demonstrate, in the general case also, that the equivalence cannot be established without the third term in the three-term photon propagator in light cone gauge.
We perform the perturbative generation of the higher-derivative Chern-Simons contribution to the effective action in the three-dimensional QED at zero and finite temperature. In the latter case, we show that as the temperature goes to infinity this contribution vanishes. However, as expected, as the temperature goes to zero only the covariant part survives. The non-covariant part contributes only in intermediate temperatures where presents a maximum.
Within the worldline approach to quantum electrodynamics (QED), a change of the photon's covariant gauge parameter $ξ$ is investigated to analyse the non-perturbative gauge dependence of the configuration space fermion correlation functions, deriving a generalization of the Landau-Kalatnikov-Fradkin transformations (LKFt). These transformations reveal how the non-perturbative gauge dependence of position space amplitudes can be absorbed into a multiplicative exponential factor.
We discuss the equivalence of the standard covariant expressions and light-front expressions of the three fundamental one loop Feynman diagrams of Quantum Electrodynamics viz. vertex correction, fermion self-energy and vacuum polarization in the light-front gauge obtained using time-ordered Hamiltonian perturbation theory. Although this issue has been addressed by us and others previously, our emphasis in this article is to resolve any ambiguity regarding the correct form of the gauge boson propagator to be used in the light-front gauge. We show how integrating over the light-front energy cons…
We explore the dependence of fermion propagators on the covariant gauge fixing parameter in quantum electrodynamics (QED) with the number of spacetime dimensions kept explicit. Gauge covariance is controlled by the the Landau-Khalatnikov-Fradkin transformation (LKFT). Utilizing its group nature, the LKFT for a fermion propagator in Minkowski space is solved exactly. The special scenario of 3D is used to test claims made for general cases. When renormalized correctly, a simplification of the LKFT in 4D has been achieved with the help of fractional calculus.
The dynamical generation of a fermion gap in graphene is studied at the infra-red Lorentz-invariant fixed point where the system is described by an effective relativistic-like field theory: reduced QED$_{4,3}$ with $N$ four component fermions ($N=2$ for graphene), where photons are $(3+1)$-dimensional and mediate a fully retarded interaction among $(2+1)$-dimensional fermions. A correspondence between reduced QED$_{4,3}$ and QED$_3$ allows us to derive an exact gap equation for QED$_{4,3}$ up to next-to-leading order. Our results show that a dynamical gap is generated for $α> α_c$ where $1.03 …
We consider the three fundamental one loop Feynman diagrams of QED viz. vertex correction, fermion self-energy and vacuum polarization in the light-front gauge and discuss the equivalence of their standard covariant expressions with the light-front expressions obtained using light-cone time-ordered Hamiltonian perturbation theory. Although this issue has been considered by us and others previously, our emphasis in this article is on addressing the ambiguity regarding the correct form of the gauge boson propagator to be used in the light-front gauge. We generalize our earlier results and show, …
We study the effect of a refined electron-photon vertex on the dynamical breaking of chiral symmetry in reduced quantum electrodynamics. We construct an educated {\em ansatz} for this vertex which satisfies the required discrete symmetries under parity, time reversal and charge conjugation operations. Furthermore, it reproduces its asymptotic perturbative limit in the weak coupling regime and ensures the massless electron propagator is multiplicatively renormalizable in its leading logarithmic expansion. Employing this vertex {\em ansatz}, we solve the gap equation to compute dynamically gener…
