Seminario. Carlos Bouthelier (DFTUZ)

"Hybrid geometrodynamics: A Hamiltonian description of QFT coupled to gravitation and foliation-dependent Hilbert space structures"

Carlos Bouthelier

Abstract:

"The Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, is generalized to the case where matter is described by a Quantum Field Theory in Curved Spacetime. Thus, in our approach there is no non-dynamic background structure and the gravitational and quantum fields have their dynamics inextricably coupled. Given the Hamiltonian nature of the framework, we must work with the generators of hypersurface deformations, represented as functions over the manifold of quantum states. A key aspect of the theory is that the Hilbert space structure of QFT is dependent on the classical gravitational degrees of freedom. Therefore, the theory is constructed in terms of a non-trivial fibration of the set of quantum states over the base manifold of gravitational variables. Another important feature of the construction is the use of Gaussian measures over the space of matter fields and of Hida distributions to define a common superspace to all possible Hilbert spaces with different measures, to properly characterize the Schrodinger wave functional picture of QFT in curved spacetime. This allows us to relate states within different Hilbert spaces in the case of vacuum states or measures that depend on the gravitational degrees of freedom, as the ones associated to Ashtekar's parametric family of complex structures. This is achieved through the inclusion of a quantum Hermitian connection for the fibration, which is necessary to be able to reproduce the Dirac's algebraic relations for the Hamiltonian generators of hypersurface deformations. Some physical features of the construction are norm conservation of the quantum states for QFT in CS (even if the total hybrid dynamics are non-unitary), the clear identification of the hybrid conserved quantities and the description of a dynamical backreaction of quantum matter on gravitation." 

Fecha: jueves, 30 de mayo de 2024
Hora: 12:00 horas
Lugar: Seminario de Física Teórica