Last update: doc. RNDr. Karel Houfek, Ph.D. (10.05.2023)
The course is covering some of the following topics: gravitational back reaction of quantized fields, effective action,
renormalization of the Green function and of the stress-energy tensor, local structure of Green functions, HaMiDeW
expansion, axiomatic approach to renormalization, approximative methods, anomalies.
Last update: doc. RNDr. Karel Houfek, Ph.D. (10.05.2023)
Přednáška bude pokrývat některá z témat: gravitačním působení kvantovaných polí, metoda efektivní akce,
renormalizace Greenovy funkce a tenzoru energie-hybnosti, lokální struktura Greenových funkcí, HaMiDeW rozvoj,
axiomatický přístup k renormalizaci, přibližné metody, anomálie.
Přednáška je určena pro studenty magisterského a doktorského programu. Navazuje na přednášku NTNF065.
Literature -
Last update: doc. RNDr. Karel Houfek, Ph.D. (09.05.2023)
Wald R. M.: Quantum Field Theory in Curved Spacetime and Black Hole (University Of Chicago Press, Chicago, 1994)
Birrell N. D., Davies P. C. W.: Quantum fields in curved space (Cambridge University Press, Cambridge, 1984)
Mukhanov V., Winitzki S.: Introduction to Quantum Effects in Gravity (Cambridge University Press, Cambridge, 2007)
Parker L., Toms D.: Quantum Field Theory in Curved Spacetime (Cambridge University Press, Cambridge, 2009)
Fulling S. A.: Aspects of Quantum Field Theory in Curved Spacetime Thermodynamics (Cambridge University Press, Cambridge, 1989)
Frolov V., Novikov I.: Black Hole Physics - Basic Concepts and New Developments (Kluwer Academic Publisher, Dordrecht, 1998)
Fabbri A., Navarro-Salas J.: Modeling Black Hole Evaporation (Imperiál College Press, London, 2005)
Jacobson T.: Introduction to Quantum Fields in Curved Spacetime and the Hawking Effect, arXiv: gr-qc/0208048 (2002)
Dewitt B. S.: Quantum Field Theory In Curved Space-Time, Phys. Rept. 19, 295 (1975)
Last update: doc. RNDr. Karel Houfek, Ph.D. (09.05.2023)
Wald R. M.: Quantum Field Theory in Curved Spacetime and Black Hole (University Of Chicago Press, Chicago, 1994)
Birrell N. D., Davies P. C. W.: Quantum fields in curved space (Cambridge University Press, Cambridge, 1984)
Mukhanov V., Winitzki S.: Introduction to Quantum Effects in Gravity (Cambridge University Press, Cambridge, 2007)
Parker L., Toms D.: Quantum Field Theory in Curved Spacetime (Cambridge University Press, Cambridge, 2009)
Fulling S. A.: Aspects of Quantum Field Theory in Curved Spacetime Thermodynamics (Cambridge University Press, Cambridge, 1989)
Frolov V., Novikov I.: Black Hole Physics - Basic Concepts and New Developments (Kluwer Academic Publisher, Dordrecht, 1998)
Fabbri A., Navarro-Salas J.: Modeling Black Hole Evaporation (Imperiál College Press, London, 2005)
Jacobson T.: Introduction to Quantum Fields in Curved Spacetime and the Hawking Effect, arXiv: gr-qc/0208048 (2002)
Dewitt B. S.: Quantum Field Theory In Curved Space-Time, Phys. Rept. 19, 295 (1975)
Syllabus
Last update: doc. RNDr. Karel Houfek, Ph.D. (10.05.2023)
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
