Instructor: Adam Helfer

Description: This course will cover conceptual developments in the theory of linear quantum fields in about the last twenty years.

Topics:

• Brief introduction to quantum theory
• Linear quantum fields; Fock space; renormalization
• Inequivalent representations of the canonical commutation relations (failure of a Stone--von Neumann theorem for quantum fields; Shale's Theorem)
• Radiation from moving mirrors; Unruh effect
• Casimir effects
• Quantum Inequalities
• Hawking effect
• Nonlinear effects and reduction (if time allows)

The course will not cover particle phenomenology.

Prerequisites: An elementary exposure to Fourier transforms, an elementary exposure to Hilbert space.

Texts (tentative): S. Fulling, Aspects of Quantum Field Theory in Curved Spacetime; R. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics