Pseudodifferential operators are ubiquitous in analysis, geometry and quantum field theory. In this course we shall focus on traces and determinants on classical pseudodifferential operators. The only traces on classical pseudodifferential operators are proportional to the Wodzicki residue which vanishes on trace-class operators. Yet we can extend the ordinary trace to a pseudo-trace on classical pseudodifferential operators, a linear form whose obstruction to being tracial we view as a tracial anomaly. The zeta determinant, which extends the ordinary determinant on determinant classes also presents an anomaly, namely the multiplicative anomaly which captures the obstruction that prevents the determinant from being multiplicative. Such tracial and determinant anomalies can often be expressed in terms of the Wodzicki residue and relate to anomalies in quantum field theory.
The lecture takes place on a weekly basis: Tuesdays 12:15 - 13:45 Room: 2.09.1.10
(Please note the change of location!)
- Kursleiter:in: Prof. Dr. Sylvie Paycha