Algebraic quantum field theory and the thermal time hypothesis
Year: 2026
Type: dissertation
Abstract: This work explores the relationship between the modular theory of von Neumann algebras and the thermal time hypothesis proposed by Carlo Rovelli and Alain Connes as a possible solution to the problem of time in quantum gravity. Starting from the algebraic formulation of quantum mechanics using C*-algebras and the developments in modular theory by Tomita and Takesaki, I motivate the usefulness of this algebraic approach across diverse fields of physics, including quantum foundations, quantum information theory, and quantum gravity. I then present the essential tools of quantum field theory through group theory, the Wightman axioms, and Weyl algebras, and finally prove the Bisognano-Wichmann theorem, which establishes the coupling of modular theory, TCP symmetries, and quantum field theory in Minkowski space. Afterwards, I consider the application of modular theory to quantum thermodynamics in the generalization of the Gibbs state to the thermodynamic limit, the KMS state. Finally, I study how the modular flow may provide a canonical interpretation of time, which is the essence of thermal time and its implications for the Unruh effect.
Author: Becerra González, Manuel
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214812012