In this paper we study the generalized electrodynamics contribution to the electron-positron scattering process e − e þ → e − e þ , i.e., Bhabha scattering. Within the framework of the standard model and for energies larger than the electron mass, we calculate the cross section for the scattering process. This quantity is usually calculated in the framework of Maxwell electrodynamics and (for phenomenological reasons) is corrected by a cutoff parameter. On the other hand, by considering generalized electrodynamics instead of Maxwell's, we show that the Podolsky mass plays the part of a natural cutoff parameter for this scattering process. Furthermore, by using experimental data on Bhabha scattering we estimate its lower bound. Nevertheless, in order to have a mathematically well-defined description of our study we shall present our discussion in the framework of the Epstein-Glaser causal theory.

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The causal perturbation theory is an axiomatic perturbative theory of the S-matrix. This formalism has as its essence the following axioms: causality, Lorentz invariance and asymptotic conditions. Any other property must be showed via the inductive method order-by-order and, of course, it depends on the particular physical model. In this work we shall study the normalizability of the generalized quantum electrodynamics in the framework of the causal approach. Furthermore, we analyse the implication of the gauge invariance onto the model and obtain the respective Ward-Takahashi-Fradkin identities.

h i g h l i g h t s• We develop the Epstein-Glaser causal approach for light-front field theory. • We evaluate in detail the vacuum polarization at one-loop for the light-front QED.• We discuss the subtle issues of the Instantaneous part of the fermionic propagator in the light-front.• We evaluate the vacuum polarization at one-loop for the light-front QED with the Instantaneous fermionic part. a b s t r a c tIn this work we show how to construct the one-loop vacuum polarization for light-front QED 4 in the framework of the perturbative causal theory. Usually, in the canonical approach, it is considered for the fermionic propagator the so-called instantaneous term, but it is known in the literature that this term is controversial because it can be omitted by computational reasons; for instance, by compensation or vanishing by dimensional regularization. In this work we propose a solution to this paradox. First, in the Epstein-Glaser causal theory, it is shown that the fermionic propagator does not have instantaneous term, and with this propagator we calculate the one-loop vacuum polarization, from this calculation it follows the same result as those obtained by the standard approach, but without reclaiming any extra assumptions. Moreover, since the perturbative causal theory is defined in the distributional framework, we can also show the reason behind our obtaining the same result DOI of original article: http://dx.1063 whether we consider or not the instantaneous fermionic propagator term.

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