Initial value formulation for a semiclassical system of interacting scalar fields

Tonatiuh Miramontes (ICN-UNAM)

RESUMEN: Quantum Gravity (QG) has remained an elusive task for a century, leaving the treatment of interacting quantum matter with gravity in a poor stance formally speaking. Quantum Field Theory on Curved Spacetimes (QFTCST) describes the behavior of quantum matter on top of a fixed background, but the ?backreaction? of the spacetime geometry due to the presence of quantum fields is an open issue generally assumed to require full QG, even for approximate descriptions, given the many issues surrounding Semiclassical Gravity. In this talk, I will elaborate a case in favor of Semiclassical Gravity, by using the QFTCST formalism to study an analogue ?toy model? of semiclassical interacting scalar fields that retains some of the formal aspects of semiclassical gravity. I will show that it is possible to recover a well posed initial value formulation for such a system. This suggests an approach towards a well posed model of semiclassical gravity, assumed to be useful as an effective theory.