Learning objectives
The goal of this course is to teach the students to understand the basis of quantum field theory.
Prerequisites
Classical and quantum mechanics
Course unit content
<u><strong>Part I (3 cfu- Prof. M. Bonini)</strong></u><br />
<p><strong>Classical field theory</strong>: Lagrangian and Hamiltonian formulations of classical mechanics and field theory. Symmetries, conserved currents and Noether's theorem.Examples of real and complex scalar field theory and electromagnetism. Wienard-Wiechert potentials, scattering Thompson, bremsstrahlung.</p>
<p><strong>Relativistic quantum mechanics</strong>: Klein-Gordon equation, negative energy solutions and the need for a quantum theory of fields. Dirac equation.<br />
Spin and representations of the Lorentz group. Properties of gamma matrices and the Dirac equation. Plane wave solutions, spin and charge of the electron and positron and charge conjugation. <br />
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<u><strong>Part II (9 cfu Prof. L. Griguolo)</strong></u><br />
<p><strong>Quantization of the free scalar field</strong><br />
Fourier decomposition and creation and annihilation operators. Fock space and spectrum. Feynman propagator. Quantization of the complex scalar field.<br />
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<p><strong>Quantization of fermion field</strong><br />
Dirac equation and action. Plane wave solutions, spin and charge of the electron and positron and charge conjugation. Quantization and anticommutation relations. The spin-statistics theorem. Parity and Time-reversal symmetries. </p>
<p><strong>Interactions</strong><br />
Introduction to interactions. Interaction picture and S-matrix. Basic Feynman diagrams for phi-to-fourth and Yukawa theories.Time-ordered products and correlation functions. Structure of spectrum, in- and out- Hilbert spaces and scattering. Kallen-Lehmann representation and renormalization. LSZ reduction formula. </p>
<p><strong>Perturbation theory and Feynman diagrams<br />
</strong>Evaluation of correlation functions in interaction picture. Wick's theorem and formulation in terms of Feynman dagrams. Evaluation of S-matrix elements.</p>
<p><strong>QED and simple scattering processes</strong><br />
Feynman diagrams for QED. Compton scattering. Electron-electron scattering. Electron-positron annihilation. Evaluations of cross-sections. <br />
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<strong>Renormalization</strong><br />
Perturbative renormalization of QED to one loop. Regularization. Ward identities. Running couplings.</p>
Full programme
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Bibliography
C. Itzykson, C. Zuber ‘‘Quantun field theory’, McGrow-Hill ed.<br />
M.Peskin, D Schroeder, ‘‘An Introduction to quantum filed theory’, Addison Welsey ed.
Teaching methods
Joined oral written exam
Assessment methods and criteria
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Other information
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