27209 - Field Theory 2

Learning outcomes

At the end of this course, the student will possess the main knowledges concerning the physical principles at the ground of the relativistic quantum field theory, of the mathematical methods of the analytic and algebraic type which stand below the models describing the quantized scalar, spinor and vector field, massive and massless, of the spatial-temporal and internal simmetries which specify the dynamics of such models. The student will become acquainted with perturbation thery for interacting quantum fields, collision theory, radiative corrections and the basic principles beyond the Standard Model of electroweak and strong interactions.

Course contents

GENERATING FUNCTIONAL.

The generating functional for the Green's functions of the real scalar free field. Symanzik functional differential equation for the generating functional of the real scalar free field and its explicit solution. Functional integration. Vacuum to vacuum transition amplitude and the determinant of a differential operator. Zeta function regularisation for the determinant of a differential operator. The fermion generating functional. Symanzik equation for fermuions. Integration over Grassmann variables. Functional integration with fermions.

FEYNMAN RULES.

Connected Green's functions. Self-interacting real scalar field. Yukawa theory. Fermion determinants. Non-relativistic Yukawa potential. Quantum electrodynamics (QED). Euclidean field theories. Non-Abelian Gauge Theories. Covariant Derivative. Nonabelian Field Strength and Yang-Mills Lagrangian. Gauge Symmetries in the Standard Model.

SCATTERING OPERATOR.

The S-matrix in non-relativistic quantum mechanics. Green's functions and the S-matrix in perturbation theory. Lehmann-Symanzik-Zimmermann reduction formulae. Cross section. Scattering amplitude. Luminosity. Quasi-elestic scattering. Electron-positron into muon-antimuon pairs. Evaluation of R:  the color hypothesis and the asymptotic freedom. Electron-muon collisions. Annihilation of an electron-positron pair into a photon pair. Compton scattering.

RADIATIVE CORRECTIONS.

Evaluation of the simplest divergent Feynman integrals. Ultraviolet cut-off regularisation. Dimensional regularisation. The photon self-energy tensor in QED. Vacuum polarization invariant function in QED. Radiative corrections to the Coulomb potential: Uheling-Serber potential, charge-screening and Lamb shift. 1-loop radiative corrections at short distances: running coupling and Landau-Pomeranchuck singularity.

Readings/Bibliography

See the up-to-dated bibliography included in the lecture notes available on-line.

Teaching methods

Front teaching.

Assessment methods

Written and oral exams.

Teaching tools

Notes are freely available on-line and continuously up-to-dated and extended with title:
Second Semester Course, Intermediate Quantum Field Theory, A Next-To-Basic Course For Primary Education.

Links to further information

http://www.robertosoldati.com

Office hours

See the website of Roberto Soldati