Quantum field theory 2

Lecturer:

Jiří Adam (gar.)

Tutor:

Jiří Adam (gar.), Jan Novotný

Supervisor:

Department of Physics

Synopsis:

Symmetries, gauge fields, spontaneous symmetry breaking, quantization of relativistic fields, reduction formulas for S-matrix elements, perturbative series, Wick theorem, radiative corrections, renormalization.

Requirements:

Knowledge of the basic course of physics, quantum physics and 02KTPE1 - Quantum field theory 1 lecture

Syllabus of lectures:

1. Lagrange formalism for free fields, symmetries and Noether theorem, space-time symmetries.

2. Gauge symmetries, non-abelian transformations, Young-Mills fields

3. Axial transformation, sigma model. Spontaneous symmetry breaking, Wigner and Goldstone modes. Explicit symmetry breaking.

4. Free scalar field, canonical commutator relations. Creation and annihilation operators, Hamiltonian, momentum and charge operators. Normal ordering, Fock space. Time-ordered products, Feynman propagator and microcausality.

5. Localized states, localized energy densities, vacuum fluctuations.

6. Quantization of free Dirac field.

Vector fields.

7. Interacting fields, (anti)commutation relations. Lehmann spectral decomposition, Young-Baxter equations.LSZ reduction formulas.

8. Perturbation series, Wick theorem, Feynman rules.

9. Several processes in tree approximation.

10. Diagrams with loops: self-energy, vacuum polarization.

11. Renormalization - general principles.

12. Renormalization of QED in one-loop.

Syllabus of tutorials:

1. Gauge symmetries, non-abelian transformations, Young-Mills fields

2. Axial transformation, sigma model. Explicit symmetry breaking.

3. Creation and annihilation operators, Hamiltonian, momentum and charge operators. Normal ordering, Fock space. Time-ordered products, Feynman propagator and microcausality.

4. Localized states, localized energy densities, vacuum fluctuations.

5. Interacting fields, (anti)commutation relations. Perturbation series, Wick theorem, Feynman rules.

6.Several processes in tree approximation, diagrams with loops: self-energy, vacuum polarization.

Study Objective:

Knowledge:

Symmetry and its violation, field quantization and S-matrix, perturbative expansion, renormalization

Abilities:

Active knowledge of field theory up to a level of one-loop renormalization of quantum electrodynamics

Study materials:

Key references:

[1] F. Gross: Relativistic Quantum Mechanics and Field Theory, Wiley-VCH, 1999; chapters 7-11

[2] J.D. Bjorken, S.D. Drell: Relativistic Quantum Fields, McGraw-Hill, 1965; chapters 11-17

[3] W. Greiner, J. Reinhardt: Field Quantization, Springer, 2008; chapters 4,5, 8 a 9

Recommended references:

[4] M.E. Peskin, D.V. Schroeder: An Introduction To Quantum Field Theory, Westview Press, 1995

[5] D.J. Griffiths: Introduction to Elementary Particles, John Wiley and sons, 1987

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: