ADVANCED TOPICS IN THE THEORY OF THE FUNDAMENTAL INTERACTIONS
This is a monographic course on Effective Field Theories (EFTs), a fundamental tool to describe a large number, if not all, physical systems. EFTs will be introduced and applied in the context
of relativistic quantum field theories, but the concepts and techniques developed here have a much wider application, covering many areas in Cosmology, Astrophysics, Nuclear Physics, Statistical Mechanics.
Solutions Test February 12, 2021
Recommended Material
Additional Material
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Notes on QFT (2018) by Marco Serone
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QFT and the Standard Model by Matthew Schwartz
Cambridge University Press 2014
Lecture Notes
Reference Program (A.Y. 2019-2020)
- CHARACTERIZATION OF A PHYSICAL SYSTEM:
degrees of freedom, symmetries, expansion parameters.
- INTEGRATING OUT HEAVY MODES: THE WILSONIAN ACTION
- EQUIVALENT EFFECTIVE LAGRANGIANS;
independence of S-matrix elements on local field redefinitions.
- SCALE DEPENDENCE IN THE EFT: anomalous dimensions; operator mixing, examples.
- EFT DESCRIBING A BROKEN PHASE:
CCWZ construction; revisitation of the chiral Lagrangian;
other examples.
Effective Program (A.Y. 2019-2020)
[3/10/2019:] General discussion about the plan of the lectures
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[10/10/2019]
Relevant, Marginal, Irrelevant operators for a relativistic QFT
in d space-time dimensions [AF: 1.2].
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[11/10/2019]
The Wilsonian action: definition; evaluation in perturbation theory;
exact result at the tree-level; examples [AF: 1.1].
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[17/10/2019]
Exercises and examples.
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[18/10/2019]
Exercises; the Fermi Lagrangian from the full electroweak theory [AM: 4.8].
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[24/10/2019]
Nonrelativistic QED: symmetries, power counting and Lagrangian in a bottom-up approach.
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[25/10/2019]
Nonrelativistic QED: tree-level matching at order 1/c^2. Scaling in nonrelativistic field theories.
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[31/10/2019]
S-matrix equivalence theorem; local field redefinitions and equivalent effective Lagrangians. Exercises. [AM: 6.1 - 6.3]
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[7/11/2019]
Proton radiuz puzzle: proton radius from the spectroscopy of ordinary and muonic atoms. Proton radius ontribution to the Lamb shift in the EFT. Rayleigh scattering.
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[8/11/2019]
Euler-Heisenberg Lagrangian in the bottom-up approach, up to dimension-8 operators. Feynman rules.
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[14/11/2019]
Matching of EH Lagrangian with QED, scalar QED and axion Lagrangian.
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[15/11/2019]
Birefringence of the vacuum; Equations of motion (EOM) of electromagnetic field from EH Lagrangian; linearization in classical background and solution.
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[21/11/2019]
Landscape and swampland of Euler-Heisemberg EFT; positivity of a1' and a2' coefficients
from analitycity, crossing symmetry and unitarity applied to light-by-light forward scattering
amplitude.
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[22/11/2019]
Exercises. Light-by-light forward scattering amplitude wiith fixed photon polarizations.
Crossing symmetry in the helicity basis and results for linearly polarized photons.
Positivity constraints on the EFT for a Goldstone mode. Equations of motions from the EH Lagrangian.
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[28/11/2019]
Low-energy EFT of a theory containing one heavy scalar and one lighy scalar. Tree-level EFT.
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[29/11/2019]
Violation of the naive scaling in the elastic amplitude for two scalars. Running coupling constant.
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[5/12/2019]
Low-energy EFT of a theory containing one heavy scalar and one lighy scalar. 1-loop EFT.
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[6/12/2019]
Emergent symmetry: Lorentz invariance as an infrared effect. Exercises.
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[12/12/2019]
Symmetries of Strong Interactions [DK: 4.1 and 4.2].
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[13/12/2019]
The chiral Lagrangian: massless quark limit and mass corrections [DK: 4.3].
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[19/12/2019]
The chiral Lagrangian: exercises. Pion elastic scattering.
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[20/12/2019]
Anomalies in QFT. Axial symmetry of QED. Anomalies of global symmetries of strong and electromagnetic interactions with 2 masless flavours.
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[9/1/2020]
Deacay of a neutral pion into two photons.
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[10/1/2020]
Callan Coleman Wess Zumino (CCWZ) formalism.
Some topics for the exam
[T]=Tree-level; [L]=1-loop