Null-plane causal perturbation theory

Quantum electrodynamics in the null-plane causal perturbation theory

“…We can interpret this result by saying that the instantaneous terms in Feynman's propagators are not physical ones, but a consequence of the splitting procedure according to a time variable whose isochronic surfaces intersect the light-cone on the entire x − -axis. Such a splitting procedure, by construction, cannot tell anything about the value of the retarded distribution at the x − -axis [60], so the instantaneous terms that arise in it cannot be relied on, but must be fixed by other conditions besides causality. As we have seen, Lorentz's covariance implies that they must not be there.…”

“…A of Ref. [60] by the method of direct construction of Fock's space and a careful choice of the basis functions in the one-particle Hilbert space, exploiting the relation with the classical Goursat's problem. Then it was obtained that the fermion quantized field operator has the following expression:…”

“…The formulation of CPT on light-front dynamics was done in Refs. [59,60], in which the causality axiom is referred to the null-plane time coordinate x + , and has been successfully applied to obtain the radiative corrections for Yukawa's model [61], directly showing the equivalence with the instant dynamics formulation [62] for that model. In view of the mentioned successes of CPT, we hope that this framework would lead to a very clear formulation of null-plane QED.…”

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

“…A in Ref. [18]-. Such a procedure had the meaning of constructing Fock's space and the operators as well as operator-valued distributions acting on it.…”

“…Aiming to shed light to the subtleties of perturbative light-front field theory, the authors developed the framework of null-plane causal perturbation theory (CPT) [17,18], an axiomatic approach to the S-matrix pro-gram initiated by Heisenberg [19] in 1943, and axiomatized in the works by Stückelberg and Rivier [20,21] and Bogoliubov, Medvedev and Polivanov [22][23][24]. The detailed perturbative solution to Bogoliubov-Madvedev-Polivanov's axioms in instant dynamics was carried out in 1973 by Epstein and Glaser [25], in a method in which the causality axiom plays an essential role, and its first application to QED was done by Scharf in 1989 [26].…”