One vertex spin-foams with the Dipole Cosmology boundary

TL;DR

This paper identifies all first-order vertex spin-foam contributions to the Dipole Cosmology transition amplitude using a general algorithm within the Operator Spin-Network Diagrams framework.

Contribution

It introduces a general algorithm to find all relevant spin-foams with fixed boundaries and internal vertices for the Dipole Cosmology model.

Findings

All first-order vertex spin-foams for the model are characterized.

The algorithm is applicable to arbitrary fixed boundary conditions.

Provides a systematic method for analyzing spin-foam contributions.

Abstract

We find all the spin-foams contributing in the first order of the vertex expansion to the transition amplitude of the Bianchi-Rovelli-Vidotto Dipole Cosmology model. Our algorithm is general and provides spin-foams of arbitrarily given, fixed: boundary and, respectively, a number of internal vertices. We use the recently introduced Operator Spin-Network Diagrams framework.