
QUANTUM FIELD THEORY
Second cycle degree in PHYSICS
Campus:
PADOVA
Language:
English
Teaching period:
Second Semester
Lecturer:
MARCO MATONE
Number of ECTS credits allocated:
6
Prerequisites:

Relativistic quantum mechanics. KleinGordon equation. Dirac equation. Canonical quantization of the scalar and fermionic fields. 
Examination methods:

The examination is oral and concerns the full programm. It starts with the explicit calculation of a Feynman diagram (phi^4 or QED) to be chosen by the student. 
Course unit contents:

INTRODUCTION. General aspects of Quantum Field Theories. Perturbative and nonperturbative formulations. Wigner and von Neumann theorems. Spontaneous symmetry breaking. Elitzur theorem. Minkowskian and euclidean formulations.
Overview of the axiomatic formulation: Wightman axioms, Wightman functions, Wightman reconstruction theorem. Schwinger functions and the OsterwalderSchroeder reconstruction theorem.
OPERATOR FORMALISM. Covariance of the Dirac equation. Spin statistics theorem. PCT theorem. The Lehman, Symanzik and Zimmerman theorem.
PATHINTEGRAL IN QUANTUM MECHANICS. Dirac paper at the basis of the Feynman idea. Forced harmonic oscillator. The vacuumvacuum amplitude. Wick rotation. Quadratic lagrangians. BohmAharonov effect.
PATHINTEGRAL FOR SCALAR THEORIES. Functional derivative. General properties of the pathintegral for scalar theories. Convergence methods Feynman propagator. Green functions. Effective action. SchwingerDyson equation. The case of phi^4. Linkedcluster theorem. Euclidean formulation. Computational techniques of functional determinants, the heat equation. Scaling properties of the coupling constant, determinants and anomaly under dilatation. Feynman rules. Computation of some Feynman diagrams for phi^4. Vertex functions and JonaLasinio theorem.
RENORMALIZATION. Ultraviolet and infrared divergences. Dimensional regularization. Superrenormalizable, renormalizable and nonrenormalizable theories. Counterterms. Relation between renormalized and bare vertex functions. Beta function. Landau pole. Ultraviolet and infrared fixed points. Asymptotic freedom and confinement.
FERMIONIC PATHINTEGRAL. Integration over Grassmann numbers. Path integral for the free fermion fields. Feynman rules for spinor fields. Fermion determinants.
QUANTUM ELECTRODYNAMICS (QED): Gauge symmetries. Feynman rules for the gauge fields. Gauge fixing. Evaluation of 1loop Feynman diagrams of QED. Ward identities. Anomalous magnetic moment of the electron.
Renormalization of the QED. 

