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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 2016/2017. |
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| 1ª Week (20/2 a 24/2) |
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. 9-28. | |
| 2ª Week (27/2 a 3/3) |
Carnival | |
| Lecture 3 | Solutions for the free particle. Spin. Projectors. Charge conjugation. Antiparticles. Dirac and Feynman-Stuckelberg interpretation of the antiparticles. Pags. 28-41. | |
| 3ª Week (6/3 a 10/3) |
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. 42-55. END of Chapter 1. |
| Lecture 5 |
Chapter 2 Propagators and Green Functions The non-relativistic propagator. Free propagators for the Dirac equation. S Matrix. Coulomb scattering. Pags. 75-88 END of Chapter 2 |
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| Series 1 | Problem series on chapters 1 and 2. Due on the 7/4/2017. | |
| 4ª Week (13/3 a 17/3) |
Lecture 6 |
Chapter 3 Feynman Rules for QED Coulomb scattering. Coulomb cross section for electrons. Theorems on the traces of gamma matrices. Pags. 89-96. |
| Lecture 7 | Explicit spin sums on the helicity basis. Coulomb scattering for positrons. Elastic electron-muon scattering. Pags. 96-104 | |
| 5ª Week (20/3 a 24/3) |
Lecture 8 | Elastic electron-muon scattering. Elastic electron-muon scattering in second order in perturbation theory. Pags. 104-112 |
| Lecture 9 |
Compton scattering. Feynman Rules for QED.
Pags. 110-115
END of Chapter 3 . 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. 127-132 |
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| 6ª Week (27/3 a 31/3) |
Lecture 10 | Summary of the second quantized free fields (continuation) Pags. 132-142. |
| Lecture 11 | S Matrix. Wick Theorem. Pags. 142-147 | |
| 7ª Week (3/4 a 7/4) |
Lecture 12 | Feynman Rules from the second quantization formalism. Pags. 148-162. END of Chapter 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 165-176 |
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| Week of Easter (10/4 a 14/4 ) |
Easter Holidays | |
| Easter Holidays | ||
| 8ª Week (17/4 a 21/4) |
Lecture 14 | Scattering electron-positron -> muon-anti-muon with helicity methods. Bhabha scattering. Bremsstrahlung. Pags 176-187 |
| Lecture 15 | Helicity amplitudes. 187-198 | |
| Series 2 | Problem series on Chapters 3 to 6. Due on the 26/5/2017. | |
| 9ª Week (24/4 a 28/4) |
Holiday (25th April) | |
| Lecture 16 | Helicity amplitudes. Crossing Symmetry. 199-208 | |
| 10ª Week (1/5 a 5/5) |
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. 219-231 |
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| 11ª Week (8/5 a 12/5) |
Lecture 19 | Scattering electron-positron -> muon-antimuon in the Standard Model. The decay of the muon. Pags. 231-239. END of Chapter 6 . |
| Lecture 20 | Practical Lecture on the installation and use of the software (with computers). | |
| 12ª Week (15/5 a 19/5) |
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. 261-266 |
| Lecture 22 | 1-loop renormalization: Self-energy of the photon (continuation). Counter terms and renormalization. Pags. 266-272 | |
| 13ª Week (22/5 a 26/5) |
Lecture 23 | 1-loop renormalization: Self-energy of the electron. Renormalization of the vertex in QED. Power counting. Renormalizable theories. Pags. 272-288 |
| Lecture 24 | Finite contributions from the renormalization: Anomalous magnetic moment of the electron. The cancelling of the infrared divergence in the Coulomb scattering. Pags. 288-297 END of Chapter 7 . | |
| Homework | Individual Homework will be available on the 26/05/2017. Due on the 5/06/2017. | |
| 14ª Week (29/5 a 2/6) |
Lecture 25 | The decay H -> photon + photon in the Standard Model: Example of a complete non trivial calculation. |
| Lecture 26 | Topic to be announced | |