Pokročilé partie kvantové teorie pole na křivém pozadí

Sylabus:

Lectures on the Heat Kernel approach in Quantum Field Theory in curved spacetime

• Schwinger-DeWitt approach vs canonical quantization
• Effective action
• Loop expansion of the effective action
• Euclidean effective action and Heat Kernel
• Lorentzian signature. DeWitt coefficients. Method Gilkey
  Example: Free fields in curved space
• Generality of assumptions about operators. Operators of the Laplace type
• Spectral functions
• Regularization and Renormalization
• Dimensional regularization. Proper time cut-off regularization. Zeta function regularization. Generalized zeta function. Zero modes contribution to the generalized zeta-function. Zeta-functions and effective action.
• Conformal anomaly. The Polyakov action.
  Example: Free 2D scalar field
  Example: 2D scalar field interacting with dilaton
• Chiral anomaly
• Remarks on the Index Theorem
• Covariant perturbation theory
• Finite temperature effects. Free energy
• Parity anomaly
• Boundaries and boundary conditions