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| The program of the discipline coincides with the text book . This text at the moment is mostly in Portuguese. |
| Aula | Program The pages numbers indicated are from the text, Introdução à Teoria do Campo by Jorge C. Romão, New edition for the academic year 2017/2018. |
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| 1ª Week (19/2 a 23/2) |
Lecture 1 | Presentation of the course: Program, bibliography and evaluation method. |
| Lecture 2 | Chapter 1 Relativistic Quantum Mechanics Dirac Equation. Covariance of the Dirac equation. Bilinear covariants. Natural system of units. The spin and the Dirac equation. Pags. 6-20. | |
| 2ª Week (26/2 a 2/3) |
Lecture 3 | Solutions for the free particle. Spin. Projectors. Charge conjugation. Antiparticles. Dirac and Feynman-Stuckelberg interpretation of the antiparticles. Pags. 20-34. |
| Lecture 4 | Spin and helicity. Equation for spin 1/2 massless particles. Minimal coupling. Lagrangian density and equations of Euler-Lagrange. Non relativistic limit of the Dirac equation. Pags. 34-44. END of Chapter 1. | |
| 3ª Week (5/3 a 9/3) |
Lecture 5 |
Chapter 2 Propagators and Green Functions The non-relativistic propagator. Free propagators for the Dirac equation. S Matrix. Coulomb scattering. Pags. 77-89 END of Chapter 2 |
| Lecture 6 |
Chapter 3 Feynman Rules for QED Coulomb scattering. Coulomb cross section for electrons. Theorems on the traces of gamma matrices. Explicit spin sums on the helicity basis. Coulomb scattering for positrons. Pags. 91-100. |
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| Series 1 | Problem series on chapters 1 and 2. Due on the 6/4/2018. | |
| 4ª Week (12/3 a 16/3) |
Lecture 7 | Elastic electron-muon scattering. Pags. 900-106 |
| Lecture 8 |
Elastic electron-muon scattering. Elastic electron-muon scattering in
second order in perturbation theory.
Compton scattering. Feynman Rules for QED. Pags. 106-115
END of Chapter 3 . |
|
| 5ª Week (19/3 a 23/3) |
Lecture 9 |
Chapter 4 S-Matrix. Wick's Theorem. Feynman Rules The Schrödinger, Heisenberg and Interaction pictures. Summary of the second quantized free fields. The real scalar field. Pags. 129-134 |
| Lecture 10 | Summary of the second quantized free fields (continuation) Pags. 134-144. | |
| Week of Easter (26/3 a 30/3) |
Easter Holidays | |
| Easter Holidays | ||
| 7ª Week (2/4 a 6/4) |
Lecture 11 | S Matrix. Wick Theorem. Pags. 144-149 |
| Lecture 12 | Feynman Rules from the second quantization formalism. Pags. 150-164. END of Chapter 4 . | |
| 8ª Week (9/4 a 13/4 ) |
Lecture 13 |
Chapter 5 Simple processes in QED Calculation of the Compton scattering cross section. Calculation of the scattering electron-positron -> muon-anti-muon. Pags 167-174 |
| Lecture 14 | Scattering electron-positron -> muon-anti-muon with helicity methods. Bhabha scattering. Bremsstrahlung. Pags 174-182 | |
| 8ª Week (16/4 a 20/4) |
Lecture 15 | Helicity amplitudes. 182-190 |
| Lecture 16 | Helicity amplitudes. Crossing Symmetry. 190-198 | |
| Series 2 | Problem series on Chapters 3 to 6. Due on the 25/5/2018. | |
| 9ª Week (23/4 a 27/4) |
Lecture 17 | Lecture on software programs used to make calculations in field theory: FeynCalc, calchep and qgraf (using the Bhabha scattering in QED as an example). END of Chapter 5 . |
| Lecture 18 |
Chapter 6 Simple Examples in the Standard Model Introduction to the Standard Model of ElectroWeak Interactions. Propagators, charged and neutral currents. decay width of the Z0 into fermions. The helicity amplitudes method for the decay of the Z0 into fermions: cases with and without mass. Pags. 227-237 |
|
| 10ª Week (30/4 a 4/5) |
Holiday (1st May) | |
| Lecture 19 | Scattering electron-positron -> muon-antimuon in the Standard Model. The decay of the muon. Pags. 237-245. END of Chapter 6 . | |
| 11ª Week (7/5 a 11/5) |
Lecture 20 | Practical Lecture on the installation and use of the software (with computers). |
| Lecture 21 |
Chapter 7 Radiative Corrections 1-loop renormalization: Self-energy of the photon (vacuum polarization). Dimensional regularization. Feynman parameterization. Wick rotation. Divergences as poles of the Gamma function. Pags. 269-274 |
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| 12ª Week (14/5 a 18/5) |
Lecture 22 | 1-loop renormalization: Self-energy of the photon (continuation). Counter terms and renormalization. Pags. 274-280 |
| Lecture 23 | 1-loop renormalization: Self-energy of the electron. Renormalization of the vertex in QED. Power counting. Renormalizable theories. Pags. 280-294 | |
| 13ª Week (21/5 a 25/5) |
Lecture 24 | Finite contributions from the renormalization: Anomalous magnetic moment of the electron. The cancelling of the infrared divergence in the Coulomb scattering. Pags. 294-303 END of Chapter 7 . |
| Lecture 25 | The decay H -> photon + photon in the Standard Model: Example of a complete non trivial calculation. | |
| Homework | Individual Homework will be available on the 25/05/2018. Due on the 4/06/2018. | |
| 14ª Week (28/5 a 1/6) |
Lecture 26 | Topic to be announced |
| Lecture 27 | Topic to be announced | |