Quantum Field Theory 1

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Physics

Synopsis:

Relativistic quantum mechanics for particles with spin 0, 1/2 a 1. Perturbative solution for one-particle equations in external field.

Feynman rules, observables in tree approximation.

Requirements:

Knowledge of the basic course of physics and of the 02KVA2B - Quantum mechanics 2 lecture

Syllabus of lectures:

1. Infinite degrees of freedom: one-dimensional string.Continuous limit, Lagrange a Hamilton formalism.

2. Klein-Gordon equation: free solutions, scalar product.Negative-energy solutions, scattering on a barrier (Klein).

3. Electromagnetic interaction in KG equation,Bound states in Coulombic potential.

4. Green function for KG equation, perturbation series.Retarded and Feynman propagators, antiparticles.

5. Feynman diagrams and Feynman rules,

Interaction and vertex factors

6. Particles with spin 1 (massive and massless),Proca equation, propagator, polarization vectors.

7. Isospin formalism.Examples (e.m. scattering of charged scalars)

8. Dirac equation: dimension, algebra of gamma-matrices, free solutions, probabilistic interpretation,

9. Dirac equation in e.m. field and Pauli limit,Covariant form of Dirac equation,

Properties of u a v spinors

10. Transformation properties of Dirac equation, bilinear forms.Dirac equation in central potential (Coulomb problem, bag model).Non-relativistic limit: Foldy-Wouthuysen transformation

11. Propagator of Dirac equation, perturbation series.Observables - traces of Dirac matrices.

12. Examples (QED processes in tree approximation).

Syllabus of tutorials:

1. One-dimensional string. Klein-Gordon equation: free solutions.

2. Electromagnetic interaction in KG equation, Green function,Retarded and Feynman propagators, antiparticles.

3. Feynman diagrams and Feynman rules, Interaction and vertex factors

4.Scattering of charged scalars, Dirac equation: dimension, algebra of gamma-matrices, free solutions, probabilistic interpretation,

5. Transformation properties of Dirac equation, bilinear forms. Dirac equation in central potential (Coulomb problem, bag model).

6. Examples (QED processes in tree approximation).

Study Objective:

Knowledge:

Relativistic one-particle equations, description of particles with various spins, Perturbative solution of equations with interaction, Feynman rules and diagrams

Abilities:

Perturbative evaluation (on the tree-level) of amplitudes and observables

Study materials:

Key references:

[1] J.D. Bjorken, S.D. Drell: Relativistic Quantum Mechanics, McGraw-Hill, 1998

[2] F. Gross: Relativistic Quantum Mechanics and Field Theory, Wiley-VCH, 1999; chapters 1-6

Recommended references:

[3] J. Formánek: Introduction to relativistic quantum mechanics and quantum field theory, Karolinum, 2000 (in Czech)

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

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: