Review of relativity, covariant formalism. Oscillation fields and their quantization: phonons. Lagrangian formalism and Noether theorem. Klein Gordon field. Electromagnetic fields and potentials: photons and their quantization in the Coulomb gauge. Interaction of matter with e.m. fields: scattering of light. Dirac’s equation for the electron, main consequences and its quantization. Superfluidity, phonon spectrum and spontaneous symmetry breaking. Superconductivity.
Notes
D. Dominici, Introductory lectures on Theoretical Physics
Prof. M. Ciafaloni, a cura di L. Fedeli, J. Giacomelli, L. Lolli
Prof. R. Casalbuoni, Quantum Field Theory
Libri: F. Mandl and G. Shaw, Quantum Field Theory, John Wiley and Sons 1984
J.J. Sakurai, Advanced Quantum Mechanics, Addison Wesley pub. Company, 1967
R. Casalbuoni, Introduction to Quantum Field Theory, World Scientific Publishing, Singapore 2011
S. J. Chang, Introduction to Quantum Field Theory, World Scientific 1990
K. Huang, Statistical Mechanics, Wiley 1987
E.M. Lifshitz and L.P.Pitaevskii, Landau and Lifshitz, Course of Theoretical Physics, Statistical Physics, part 2, Pergamon Press
A.L. Fetter and J.D. Walecka, Quantum Theory of Many-Particle Systems, McGraw-Hill 1971
M. Tinkham, Introduction to Superconductivity, Krieger Pub.
Learning Objectives
Review of relativity, covariant formalism. Oscillation fields and their quantization: phonons. Lagrangian formalism and Noether theorem. Klein Gordon field. Electromagnetic fields and potentials: photons and their quantization in the Coulomb gauge. Interaction of matter with e.m. fields: photon emission and absorption, scattering of light. Superfluidity, phonon spectrum and spontaneous symmetry breaking. Dirac’s equation for the electron, main consequences and its quantization.
Oscillation fields and their quantization: phonons.
Linear chain.
Lagrangian and Hamiltonian. Continuous limit. Quantization.
Brief review of covariant formalism of special relativity. Covariant form of Maxwell equations.
Lorentz equation.
Quantization of the Klein Gordon field
Noether theorem and applications.
Dirac field
Dirac’s equation for the electron, main consequences and its quantization. Energy projectors. Covariance of Dirac equation.
Parity. Charge conjugation. Quantization of Dirac field. Spin Statistics. Higgs decay in two fermions. mu decay.
Electromagnetic field
Maxwell equations. Lorentz and Coulomb gauge. Lagrangian and Hamiltonian in the Coulomb gauge. Quantization.Photons.
Interaction of matter with e.m. fields. Coherent states.
Casimir effect.
Scattering theory.
S matrix. Dyson series. Fermi golden rule.
Matter radiation interaction.
Lagrangian and Hamiltonian for a set of non relativistic charged particles.
Cherenkov effect, scattering of light (Thomson, Rayleigh e Raman).
Superfluidity
Bose Einstein condensation. Schrodinger field.
Phonon spectrum and spontaneous symmetry breaking. Landau and Bogoliubov approach.
Superconductivity
Cooper pairs and BCS Hamiltonian.