2024
Quantum Field Theory-2 (13 lectures at the EPFL, spring)
Advanced Quantum Field Theory (13 Lectures at the EPFL, fall)
2023
Advanced Quantum Field Theory (13 Lectures at the EPFL)
Quantum Field Theory -1 (at the master-II of ICFP, same as n 2022)
2022
Quantum Field Theory -1 (at the master-II of ICFP, ENS Paris)
Lectures notes (for in-person student only)
L1, Why QFT
L2-part1, Lagrangian and Hamiltonian for fields, Klein-Gordon as best guess at long distances
L2-part2, Canonical quantization free real scalar field, particle interpretation and bose statistic,
construction Lorentz generators
L3, Canonical quantization Charged scalar field, Wightman functions, Feynman's correlator,
Lorentz invariance and causality
L4, Axioms of scalar QFT, Kallen-Lehmann spectral rep., analytic structure 2-point
correlators
and dispersion relations
L5, Perturbation theory and Dyson series, Causality vs Lorentz invariance
L6, Wick theorem, Feynman's diagrams in position and momentum space , momentum
conservation, tree vs loop diagrams
L7, Loops-expansion=coupling-expansion, quantum correction interpretation,
NDA, renormalization first encounter: the tadpole
L8, Functional generators Z[J] and W[J], Feynman's diagrams with charged fields
L9-part 1, Theory of Scattering and LSZ reduction
L9-part 2, LSZ reduction, Amputation and wavefunction renormalization, crossing symmetry
L10, Fields as Lorentz irreps, Weyl spinors, Sigma matrices, Dirac Spinors and gamma-matrices, Diracology
L11, Weyl, Dirac and Majorana actions and e.o.m., quantizing free Dirac,
spin-statistics, positivity of energy, causality with fermions, Wick theorem and Feynman diagrams with Dirac
L12, Massive vector field, eliminate spin-0 state, 3 polarizations and the little group SU(2), Hamiltonian and quantization,
propagator and the LSZ
L13 part -1, Massless vectors and the Photon: longitudinal polarization blowing up, current conservation,
gauge invariance as redundancy, Ward identity as consistency condition,
ISO(2) little group and triviality translations, gauge invariance from Lorentz-invariance and finite d.o.f., propagator
L13 part-2, QED as EFT of 2 oppositely charged Weyl fermions coupled to massless spin-1,
accidental P, C and T discrete symmetries of QED, transformations of fermion bilinears,
perturbative proof of CPT theorem
L14 parts_1,2 and 3: intro perturbative renormalization, Wick rotation, 1-loop corrections to the self-energy in phi^4,
1-loop corrections to the coupling in phi^4, locality of counter-terms and predictions on non-analytic terms,
checking the optical theorem at 1-loop, Feynman parametrization, the meaning of renormalization,
various regularisations, dimensional reg.
L15 effective action (skipped)
L16 part 1 and 2: -1-loop in phi^3 in D=6: self-energy and vertex renormalization, photon self-energy in QED,
photon transversity via charge conservation, 1PI resummation self energy in QED,
wave function renormalization, 1 loop QED self-energy in dim reg.,
renormalization of coulomb potential: short and long distance corrections,
vacuum polarization and hint to running coupling
L17 Renormalization group equation, beta functions, beta function in phi^4 in D=4, beta function in phi^3 in D=6,
resumming large logs, asymptotics of QFTs: beta>0, beta<0, beta=0, Landau pole and asymptotic freedom,
QED beta function via renormalised potential, QED beta function via renormalized self-energy
L18, part 1 and 2: Path integral in QM: from Euclidean to Minkowski, Gaussian Integration,
2pt-function harmonic oscillator via path integral , Path integral in QM for scalars,
2pt function for scalars via Gaussian integration, perturbative expansion and Dyson series via path int.,
Photon propagator via path integral and gauge fixing
2021
Advanced QFT (10 Lectures at the EPFL)
2020
Topics in EFT (PhD course in Rome) (lecture notes here)
L1 Introduction to EFT via QM anharmonic oscillator
L2 Examples of 4D EFT (massless fermion and massless photon), matching and universality
L3 Scale transformations, irrelevant vs relevant perturbations, intro to Wilsonian RG-flow, phi^4 beta function
L4 Fast and slow modes, running of the mass term, anomalous dimensions, Wilson-Fisher fixed point
L5 UV sensitivity and naturalness, symmetries and spurions, technical vs natural
L6 Massless spin-1 and spin-2 particles, Little group, Locality+Lorentz+causality require gauge transformations
L7 Weinberg's Soft-theorems, electric charge conservation and equivalence principle from consistency of soft amplitudes, bootstrapping Yang-Mills theory
L8 Bootstrapping GR for the m=0 spin-2 self-interacting particle, using first-order formalism.
L9 Field Redefinitions and E.o.m., EFT for photons and gravitons, estimate strong coupling scales, leading higher-derivative corrections to Einstein-Maxwell EFT
L10 Causality and unitarity constraints in EFT
QFT-II (master ICFP at the ENS, Paris )
TD-1 Yang-Mills theory from consistency of Gauss law and 1st order formalism, Noether Theorem and conserved currents;
TD-2 Yang-Mills theory from consistency of Compton scattering via on-shell method (+ discussion homework)
TD-3+4 Ward identities, Global charges, spontaneous breaking and Goldstone theorem (+ discussion homework)
TD-5+6 Goldstone EFT, Higgs mechanism, and equivalence theorem, mostly for U(1) theory (+ discussion homework)
TD-7+8 cancelled
Homework: 1, 2, 3, 4, 5 (solutions: 1, 2, 3, 4, 5)
GGI School: Theory of fundamental Interactions: lectures, webpage
2019
QFT-II (master ICFP at the ENS, Paris )
TD-1 Non-abelian gauge theory from consistency of factorization in Compton scattering
TD-2 Yang Mills from consistency of Gauss law and 1st order formalism; Noether theorem, conserved currents and Ward-Takahashi identies
TD-3 Spontaneous breaking and Goldstone bosons
TD-4 solutions homework-3
TD-5 Higgs mechanism and Equivalence Theorem
TD- 6 Anomalies via path integral, anomaly cancellation in the SM, pi0 decay into gammas
GGI school Theory of Fundamental Interactions: website
2018
Aspects of (micro)causality in EFTs (at TUM)
causality and Lorentz, via Kallen-Lehmann, via Wick rotation, linear response theory, analyticity 2pt functions, analyticity refraction index, forward scattering, causality vs analyticity, dispersion relations, positivity bounds for scattering amplitudes
Advanced Topics in the Theory of Fundamental Interactions (at the University of Padova)
(lecture notes here)
L1: dimensional analysis, intro to EFTs, Integrating out and tree-level matching
L2: Wilsonian effective action, decoupling, RG and beta-functions, Wilson-Fisher, anomalous dim
L3+L4: decoupling in QED, Landau pole, Banks-Zaks, UV sensitivity and naturalness, symmetries and spurions, chiral symmetry, estimating the cutoff and spurion analysis, technical vs natural, hbar counting, g-2
L5+L6: running in QCD, chiral symmetry breaking and Goldstone bosons, chiral effective theory, matching currents, Gell-Mann-Okubo, masses from quark mass splittings and electromagnetic interactions
L7+L8: CCWZ, cosetology, Goldeberger-Treiman, matching currents and neutron decay, unitarizations, rho-meson and photon mixing
L9: Higgs mechanism, restoring gauge invariance for massive spin-1 fields, equivalence theorem
Gauge Theory of the Electroweak Interactions (master-2 ICFP at the ENS, Paris )
GGI school Theory of Fundamental Interactions: website
2017, 2016
Gauge Theory of the Electroweak Interactions (master-2 ICFP at the ENS, Paris )
GGI school Theory of Fundamental Interactions: website
2014
Higgs Physics in the SM and Beyond (PhD-school edpif at IPhT Saclay)