Physical representations for scattering amplitudes and the wavefunction of the universe
Abstract
The way we organise perturbation theory is of fundamental importance both for computing the observables of relevance and for extracting fundamental physics out of them. If on one hand the different ways in which the perturbative observables can be written make manifest different features (e.g. symmetries as well as principles such as unitarity, causality and locality), on the other hand precisely demanding that some concrete features are manifest lead to different ways of organising perturbation theory. In the context of flatspace scattering amplitudes, a number of them are already known and exploited, while much less is known for cosmological observables. In the present work, we show how to systematically write down both the wavefunction of the universe and the flatspace scattering amplitudes, in such a way that they manifestly show physical poles only. We make use of the invariant definition of such observables in terms of cosmological polytopes and their scattering facet. In particular, we show that such representations correspond to triangulations of such objects through hyperplanes identified by the intersection of their facets outside of them. All possible triangulations of this type generate the different representations. This allows us to provide a general proof for the conjectured allloop causal representation of scattering amplitudes. Importantly, all such representations can be viewed as making explicit a subset of compatible singularities, and our construction provides a way to extend Steinmann relations to higher codimension singularities for both the flatspace scattering amplitudes and the cosmological wavefunction.
 Publication:

SciPost Physics
 Pub Date:
 June 2022
 DOI:
 10.21468/SciPostPhys.12.6.192
 arXiv:
 arXiv:2112.09028
 Bibcode:
 2022ScPP...12..192B
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology;
 Mathematical Physics;
 Mathematics  Combinatorics
 EPrint:
 18 pages, 10 figures. v2: corrected a few typos