Quantum electrodynamics in the null-plane causal perturbation theory

Quantum electrodynamics in the null-plane causal perturbation theory. II.

“…As we have seen in Ref. [29], the gauge terms of the radiation field commutation distribution do not contribute to Møller's scattering, which is an expression of gauge invariance. It is our aim in this section to prove that they in fact do not contribute to any process, in other words, that the scattering operator can be constructed with the covariant terms only.…”

“…As we observe, the commutation distribution of the radiation field already contains nonlocal terms (gauge terms). This is different to what happens with the fermion field anticommutation distribution: It is covariant, and the nonlocal term appears only in its retarded part [29]. Therefore, since in the causal approach the causal distributions contain products of the positive-and negativefrequency parts of the (anti)commutation distributions of the quantized fields, the instantaneous term of the fermion field does not appear in loop calculations, a fact that was exploited in Yukawa's model [27] and for the calculus of vacuum polarization in QED [29].…”

“…The procedure to obtain Ward-Takahashi's identities is as in the instant dynamics formulation [38]. Recall [29] that the one-point distribution for QED only contains the interaction between the gauge field and the matter fields:…”

“…x 2 ), and which has been implicitly used in our previous paper, Ref. [29], in order to normalize the vacuum polarization scalar only, leaving unchanged the tensor structure.…”

“…In a previous paper [29], that started the series of which the present one is the second part, the authors started the study of QED in light-front dynamics in the framework of null-plane CPT, in which the equivalence with instant dynamics was accomplished for the scattering processes and vacuum polarization, when gauge invariance is taken into account. More precisely, we have seen that the photon quantized field operator in the null-plane gauge is -we use latin indices a, b, c, • • • to denote the null-plane components of vectors (a = +, 1, 2, −)-:…”