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.
Notes 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. Lagrangian of a relativistic particle in a covariant form.
Quantization of the Klein Gordon field. Noether theorem and applications.
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 fields and potentials: photons and their quantization in the Coulomb gauge. Interaction of matter with e.m. fields. Coherent states. S matrix. Dyson series. Fermi golden rule. Casimir effect. Cherenkov effect , scattering of light.
Superfluidity, phonon spectrum and spontaneous symmetry breaking. Landau and Bogoliubov approach.