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Register a new userLandau-Khalatnikov-Fradkin transformations in Reduced Quantum Electrodynamics
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Jesus Javier Cobos Martinez
Publication date
2016
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English
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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$_{d_gamma,d_e}$.
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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.
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.
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 $QED_3$.
An alternative approach to solving the Landau-Khalatnikov problem on one-dimensional stage of expansion of hot hadronic matter created in collisions of high-energy particles or nuclei is suggested. Solving the relativistic hydrodynamics equations by the Riemann method yields a representation for Khalatnikovs potential which satisfies explicitly the condition of symmetry of the matter flow with respect to reflection in the central plane of the initial distribution of matter. New exact relationships are obtained for evolution of the density of energy in the center of the distribution and for laws of motion of boundaries between the general solution and the rarefaction waves. The rapidity distributions are derived in the Landau approximation with account of the pre-exponential factor.
An approach that has been given promising results concerning investigations on the physics of graphene is the so-called reduced quantum electrodynamics. In this work we consider the natural generalization of this formalism to curved spaces. We employ the local momentum space representation. We discuss the validity of the Ward identity and study one-loop diagrams in detail. We show that the one-loop beta function is zero. As an application, we calculate the one-loop optical conductivity of graphene by taking into account curvature effects which can be incorporated locally. In addition, we demonstrate how such effects may contribute to the conductivity. Furthermore, and quite unexpectedly, our calculations unveil the emergence of a curvature-induced effective chemical potential contribution in the optical conductivity.
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