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Register a new userLandau-Khalatnikov-Fradkin transformation for the fermion propagator in QED in arbitrary dimensions
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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.
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We derive the Landau-Khalatnikov-Frandkin transformation (LKFT) for the fermion propagator in quantum electrodynamics (QED) described within a brane-world inspired framework where photons are allowed to move in $d_gamma$ space-time (bulk) dimensions, while electrons remain confined to a $d_e$-dimensional brane, with $d_e < d_gamma$, referred to in the literature as reduced quantum electrodynamics, RQED$_{d_gamma,d_e}$. Specializing to the case of graphene, namely, RQED$_{4,3}$ with massless fermions, we derive the nonperturbative form of the fermion propagator starting from its bare counterpart and then compare its weak coupling expansion to known one- and two-loop perturbative results. The agreement of the gauge-dependent terms of order $alpha$ and $alpha^{2}$ is reminiscent from the structure of LKFT in ordinary QED in arbitrary space-time dimensions and provides strong constraints for the multiplicative renormalizability of RQED$_{d_gamma,d_e}$.
The Landau-Khalatnikov-Fradkin transformations (LKFTs) represent an important tool for probing the gauge dependence of the correlation functions within the class of linear covariant gauges. Recently these transformations have been derived from first principles in the context of non-Abelian gauge theory (QCD) introducing a gauge invariant transverse gauge field expressible as an infinite power series in a Stueckelberg field. In this work we explicitly calculate the transformation for the gluon propagator, reproducing its dependence on the gauge parameter at the one loop level and elucidating the role of the extra fields involved in this theoretical framework. Later on, employing a unifying scheme based upon the BRST symmetry and a resulting generalized Slavnov-Taylor identity, we establish the equivalence between the LKFTs and the Nielsen identities which are also known to connect results in different gauges.
In this work we report on the Landau gauge photon propagator computed for pure gauge 4D compact QED in the confined and deconfined phases and for large lattices volumes: $32^4$, $48^4$ and $96^4$. In the confined phase, compact QED develops mass scales that render the propagator finite at all momentum scales and no volume dependence is observed for the simulations performed. Furthermore, for the confined phase the propagator is compatible with a Yukawa massive type functional form. For the deconfined phase the photon propagator seems to approach a free field propagator as the lattice volume is increased. In both cases, we also investigate the static potential and the average value of the number of Dirac strings in the gauge configurations $m$. In the confined phase the mass gap translates into a linearly growing static potential, while in the deconfined phase the static potential approaches a constant at large separations. Results shows that $m$ is, at least, one order of magnitude larger in the confined phase and confirm that the appearance of a confined phase is connected with the topology of the gauge group.
By applying an inverse Landau-Khalatnikov transformation, connecting (resummed) Schwinger-Dyson treatments in non-local and Landau gauges of $QED_3$, we derive the infrared behaviour of the wave-function renormalization in the Landau gauge, and the associated critical exponents in the normal phase of the theory (no mass generation). The result agrees with the one conjectured in earlier treatments. The analysis involves an approximation, namely an expansion of the non-local gauge in powers of momenta in the infrared. This approximation is tested by reproducing the critical number of flavours necessary for dynamical mass generation in the chiral-symmetry-broken phase of $QED_3$.
We evaluate the fermion propagator in parity-conserving QED_3 with N flavours, in the context of an IR domain approximation. This provides results which are non-perturbative in the loopwise expansion sense. We include fermion-loop effects, and show that they are relevant to the chiral symmetry breaking phenomenon, that can be understood in this context.
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