The Department of Logic & Philosophy of Science Colloquium Series presents
"Noether's Theorems in AQFT"
with Noel Swanson, Philosophy Department, Princeton University
Thursday, May 8, 2014
Social Science Tower, Room 777, LPS conference room
Noether's two theorems establish a tight link between symmetries and conserved quantities
in classical field theory. Extending these results to quantum field theory has proven
challenging due to the intricacies of
renormalization and the presence of anomalies. In this talk, Swanson will explain how a version of Noether's first theorem can be obtained in the setting of algebraic quantum field theory (AQFT). Given a field system satisfying the split property and a global gauge symmetry (or global space-time symmetry), we can canonically construct local generators which induce the given symmetry on the local observable algebras. We can then go on to build conserved currents from these generators.
This result has a number of important consequences. First, it allows us to import tools from DHR analysis (originally designed to describe global charge structure) to characterize local charge structure. Second, it gives us a recipe for recovering a local Hamiltonian dynamics from the global algebraic dynamics. Swanson will argue that we should expect these consequences to carry over to the more physically relevant case of field systems with local gauge symmetry. Swanson will conclude by discussing prospects for establishing a corresponding AQFT-analogue of Noether's second theorem.
For further information, please contact Patty Jones, firstname.lastname@example.org or 949-824-1520.