Causality and Unitarity via the Tree-Loop Duality Relation
High Energy Physics - Theory
2017-09-13 v2 High Energy Physics - Phenomenology
Abstract
The tree-loop duality relation is used as a starting point to derive the constraints of causality and unitarity. Specifically, the Bogoliubov causality condition is ab initio derived at the individual graph level. It leads to a representation of a graph in terms of lower order cut graphs. Extracting the absorptive part gives then the general unitarity relation (Cutkosky rule). The derivation, being carried out directly in momentum space, holds for any local (polynomial) hermitian interaction vertices. This is in contrast to the technical difficulties arising from contact terms in the spacetime approach based on the largest time equation.
Keywords
Cite
@article{arxiv.1701.07052,
title = {Causality and Unitarity via the Tree-Loop Duality Relation},
author = {E. T. Tomboulis},
journal= {arXiv preprint arXiv:1701.07052},
year = {2017}
}
Comments
23 pages, 5 figures, typos corrected, some added references and concluding remarks, published version