. – Theoretical physics
PROFESSOR GIUSEPPE NARDELLI
Text under revision. Not yet approved by academic staff.
COURSE AIMS
The main aim of the course is to introduce students to the study of perturbation
theory in the context of quantum field theory (S-matrix, Feynman diagrams and
cross sections). The whole content is dealt with by applying the formalism of path
integrals restricted - to avoid technical difficulties - to the case of scalar fields. The
corresponding formulas and applications of spinor electrodynamics are dealt with
in any case (but not derived). Renormalization and the renormalization group
equations and their consequences are also introduced.
COURSE CONTENT
Two-point functions and their physical meaning.
Cubic scalar perturbation theory.
LSZ formula. Path integrals for free fields and interacting fields, Feynman rules
and scattering amplitudes. Calculation of quantum amplitudes, Mandelstam
variables, cross sections and decay times.
Källén-Lehmann spectral representation. Loop corrections in the scalar theory and
overview of renormalizability. Extension to spinor electrodynamics: Lamb shift.
Infrared divergences and subtraction schemes. Renormalization group equations
and asymptotic freedom (scalar fields).
Resonances, unstable particles and decay.
Effective action.
Path integrals for fermions, Grassmann variables, and path integrals for vector
fields.
Symmetries in quantum systems, and Ward and Ward-Takahashi identities.
Broken symmetry in quantum systems: Chiral anomaly.
READING LIST
M. SREDNICKI, Quantum Field Theory, Cambridge Univ. Press, 2007.
L.H. RYDER, Quantum Field Theory, Cambridge Univ. Press, 1985.
M. PESKIN AND D.V. SCHROEDER, An introduction to Quantum Field Theory, Westview 1995.
K. HUANG, Quantum Field Theory (from operators to path integrals), J. Wiley and Sons, 2004.
TEACHING METHOD
Lectures.
ASSESSMENT METHOD
Oral examination.
NOTES
Further information can be found on the lecturer's webpage
http://www2.unicatt.it/unicattolica/docenti/index.html or on the Faculty notice board.
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