Learning objectives
The main theme of this course is the idea and application of renormalization group. This course includes path integral quantization, regularization, renormalization, non-Abelian gauge theories, spontaneous symmetry breaking. The goal is to compute the beta function in on-Abelian gauge theories and discuss asymptotic freedom.
Prerequisites
Quantum field theory I (Teoria quantistica dei campi I)
Course unit content
<p><strong><br />
Functional methods</strong> Path integrals in quantum mechanics and quantum field theory.
Perturbation theory and Feynman diagrams.
Feynman rules from path integrals.
Fermions and Grassman variables.</p>
<p><br />
<strong>Renormalisation
</strong> Ultraviolet divergences and regularisation. Dimensional regularisation.
Renormalised perturbation theory. Renormalisation group. Renormalization condition
Beta functions and anomalous dimensions, IR/UV fixed points, Callan-Symanzik equation.
1PI effective action. Derivative expansion of 1PI effective action; Effective potential. Spontaneous symmetry breaking, Nambu-Goldstone theorem - proof by 1PI effective action and Ward identity.</p>
<p><br />
<strong>Non-Abelian gauge field theory</strong>
Abelian and non-Abelian gauge symmetries.
QCD and Yang-Mills theory.
Gauge fixing and Faddeev-Popov ghosts.
Computation of the beta function.
Asymptotic freedom, colour confinement and the continuum limit.<br />
<br />
</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
Homeworks. Final exam (written and oral)
Assessment methods and criteria
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Other information
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