Seminario Q-Math
Geometric Flavours of Quantum Field Theory: Modifications to the Schrödinger Equation and Applications to Cosmology
Ponente: David Martínez Crespo (Universidad de Zaragoza)Fecha: martes 26 de noviembre de 2024 - 13:00Lugar: Room 2.2.D08, Universidad Carlos III de Madrid
Online: https://eu.bbcollab.com/guest/22f7877a774148a3aee3e398a4a86380 (active on request)
Resumen:
In this talk, we will apply the geometrization of quantum field theory to explore its implications in curved backgrounds. In this program, the Schrödinger-like Hamiltonian equations of QFT are understood as a Hamiltonian flow in the manifold of pure states. This is an infinite-dimensional Kähler manifold representing the Schrödinger-like wavefunctions. In the case of curved backgrounds, this Kähler structure acquires a dependence on the Hamiltonian time parameter that, by relying solely on the Hamiltonian flow, jeopardizes the probabilistic interpretation of quantum theory. To overcome this difficulty, we describe the program of geometric quantum field theory (not to be confused with the geometrization program), explore its different representations, and propose modifications to the family of Schrödinger-like equations. The mathematical foundations of this study depend not only on differential geometry but also on the theory of Gaussian integration in topological vector spaces. As a consequence of this study, we will present applications of the formalism to cosmological Friedman-Lemaître-Robertson-Walker solutions of General Relativity.
