Quantum Field Theory 1
Code  Completion  Credits  Range 

02QFT1  Z,ZK  7  4+2 
 Lecturer:
 Jiří Adam (guarantor)
 Tutor:
 Zdeněk Hubáček
 Supervisor:
 Department of Physics
 Synopsis:

Relativistic quantum mechanics for particles with spin 0, 1/2 a 1. Perturbative solution for oneparticle 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: onedimensional string.Continuous limit, Lagrange a Hamilton formalism.
2. KleinGordon equation: free solutions, scalar product.Negativeenergy 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 gammamatrices, 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).Nonrelativistic limit: FoldyWouthuysen transformation
11. Propagator of Dirac equation, perturbation series.Observables  traces of Dirac matrices.
12. Examples (QED processes in tree approximation).
 Syllabus of tutorials:

1. Onedimensional string. KleinGordon 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 gammamatrices, 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 oneparticle equations, description of particles with various spins, Perturbative solution of equations with interaction, Feynman rules and diagrams
Abilities:
Perturbative evaluation (on the treelevel) of amplitudes and observables
 Study materials:

Key references:
[1] J.D. Bjorken, S.D. Drell: Relativistic Quantum Mechanics, McGrawHill, 1998
[2] F. Gross: Relativistic Quantum Mechanics and Field Theory, WileyVCH, 1999; chapters 16
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 timetable has been prepared for this course
 The course is a part of the following study plans:

 Experimentální jaderná a částicová fyzika (compulsory course of the specialization)