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Course, academic year 2018/2019
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Advanced topics in quantum field theory on curved background - NTMF095
Title in English: Pokročilé partie kvantové teorie pole na křivém pozadí
Guaranteed by: Institute of Theoretical Physics (32-UTF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: not taught
Language: English
Teaching methods: full-time
Additional information: http://utf.mff.cuni.cz/vyuka/TMF095/
Guarantor: prof. RNDr. Pavel Krtouš, Ph.D.
prof. Andrei Zelnikov
Annotation -
Last update: T_UTF (10.05.2012)
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.
Literature -
Last update: T_UTF (10.05.2012)

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: prof. RNDr. Pavel Krtouš, Ph.D. (22.02.2016)

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
 
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