Speaker
Description
Epstein-Glaser’s ideas for the formulation of a distributional well-defined perturbative causal field theory are developed in light-front dynamics over the invariant null-plane coordinatization introduced by Rohrlich. Explicitly, the causality theorems which warrant the method are shown to remain valid in that dynamics, and the causal distribution splitting formulae are re-derived in accordance with it, exhibiting important differences with respect to its instant dynamics version. Application of these splitting formulae to the commutation distributions of the fermion and radiation fields naturally leads to the well known instantaneous terms of their Feynman’s propagators, while the scalar field’s one retains its form from instant dynamics. Additionally, the developed method is applied to scalar QED at second order, taking for the first order distribution the interaction only with the linear in the coupling constant part of the current. We analyse Moeller’s scattering, for which the equivalence with instant dynamics is established, and Compton’s scattering, for which the vertex coming from the second order term in the current is automatically generated in the normalization procedure once the residual gauge invariance which remains from the imposition of the null-plane gauge condition is exploited.
References
[1] H. Epstein, V. Glaser. The role of locality in perturbation theory. Ann. Inst. H. Poincaré A 19: 211-295, (1973).
[2] F. Rohrlich. Null Plane Field Theory. Acta Phys. Austriaca, Suppl. VIII, 277-322, (1971).
[3] G. Scharf. Finite Quantum Electrodynamics. The Causal Approach. 3th Edition. Dover, (2014).
[4] R. Bufalo, B.M. Pimentel, D.E. Soto. The Epstein-Glaser causal approach to the light-front QED4. I: Free theory. Ann. Phys. 351: 1034-1061, (2014).
[5] R. Bufalo, B.M. Pimentel, D.E. Soto. The Epstein-Glaser causal approach to the light-front QED4. II: Vacuum polarization tensor. Ann. Phys. 351: 1062-1084, (2014).
