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Detailed Programme of the Week 10/25/2021 -- 10/29/2021:

-- Classical Fields

LECT 22-23  -- Tuesday 10/26/2021 - 2h Bonciani    14:00-16:00   (Conversi)  meet.google.com/szf-gndu-pwc

Recap of finite-dimensional representation of the Lorentz group. One-particle states. Pauli-Lubanski vector. Massive and massless particles. Helicity. Infinite dimensional representations of the Poincare' group.



LECT 24-25 -- Thursday 10/28/2021 - 2h Bonciani    14:00-16:00   (Conversi)  meet.google.com/szf-gndu-pwc

Natural Units. Klein-Gordon (KG) Equation. Motivations. Recapitulation of Schroedinger's Equation and non relativistic QM point of view. The scalar product in L2 and its time independence. Covariance of the KG equation. Scalar product for the KG field and probability density not positive definite. Lagrangian and Hamiltonian of the KG field. Charged scalar field and global U(1) symmetry. Charge conserved and scalar product.


LECT 26 -- Friday 10/29/2021 - 1h Bonciani    8:00-9:00  (Majorana)  meet.google.com/rkn-mafj-mra

Potential in the Lagrangian and mass term. Plane wave solutions of the KG equation. Positive and negative energy solutions. Normalization of the solutions and ortonormal basis. General solution as superposition of positive and negative energy solutions. Canonical Quantization. Conjugated momenta, Hamiltonian density, probability density. Change of perspective and quantization. Field in terms of creation and annihilation operators.