Note on Emergent Canonical Typicality in Group Field Theory

Abstract

We study the emergence of canonically typical states in the group field theory approach to quantum gravity. Based on the Page-Wootters formalism for emergent relational time/dynamics in a closed quantum system that has been recently generalized to group field theory, we can derive the emergent canonically typical states by choosing a complex relational time parameter. When the time parameter can be related to the spacetime diffeomorphism of the to be emerged spacetime, the canonically typical states can be interpreted as the thermal states of group field theory, which then greatly simplifies the previous constructions of thermal states for group field theory found in the literature.