Abstract
We examine the non-perturbative gauge dependence of arbitrary configuration space fermion correlators in quantum electrodynamics (QED). First, we study the dressed electron propagator (allowing for emission or absorption of any number of photons along a fermion line) using the first quantised approach to quantum field theory and analyse its gauge transformation properties induced by virtual photon exchange. This is then extended to the $N$-point functions where we derive an exact, generalised version of the fully non-perturbative Landau-Khalatnikov-Fradkin (LKF) transformation for these correlators. We discuss some general aspects of application in perturbation theory and investigate the structure of the LKF factor about $D = 2$ dimensions.
Highlights
The nonperturbative structure of the N-point functions in quantum electrodynamics (QED) is an important aspect of quantum field theory, yet analyzing such aspects of the theory remains a difficult problem and still attracts significant attention
II, we review the precise form of the LKF transformations and recent work on their application
This section has focused on perturbation theory in configuration space, it is possible to transfer the LKF transformations found here to the perturbative expansion in momentum space. This has been achieved for the propagator in scalar and spinor QED in D 1⁄4 3 and D 1⁄4 4 dimensions [38,105,108]; the generalization we have developed here will allow us to apply these techniques to arbitrary correlation functions in future work
Summary
The nonperturbative structure of the N-point functions in QED is an important aspect of quantum field theory, yet analyzing such aspects of the theory remains a difficult problem and still attracts significant attention. This article expands upon the brief report of the main results given in [63], where we sought to compare the forms of the generalized transformation of the N-point functions between spinor and scalar QED; second, the theoretical developments presented here for spinor QED are far from trivial and will serve as a stepping stone to the more complicated transformations in QCD or more general gauge theories (worldline techniques have been extended to the non-Abelian case in a series of recent articles [93,94,95,96,97,98]); a systematic study of the variation of N-point functions under a change of gauge is crucial for understanding how gauge invariant information can be extracted from calculations carried out in particular gauges—we have in mind, for instance, the truncation of Dyson-Schwinger equations to a particular order or numerical evaluation of such quantities on the lattice. Our use of the worldline formalism will be seen to simplify both the derivation of the LFK transformations and their implementation in perturbation theory
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