ADVANCED QUANTUM FIELD THEORY

1) INTRODUCTION TO QUANTUM FIELD THEORY. Perturbative and axiomatic aspects.
2) CONSISTENT QUANTUM INTERACTIONS. Coleman-Mandula theorem. Characteristics of interactions versus particle spin. Axion-scalar field duality.
3) CLASSICAL FIELD THEORIES. Action and equations of motion. Universality of couplings. Chiral and Yukawa couplings. Global symmetries and Noether theorem. Theories with local abelian and non-abelian symmetries. Yang-Mills (YM) connection and field strength. Covariant derivative. Conserved currents and covariant currents. Self-interaction of YM fields. Color charge.
4) FUNCTIONAL INTEGRAL METHODS. Brief review of basic concepts. Generating functionals. Analyticity and euclidean space. Background field method. Linear classical symmetries and their quantum implementation. Applications to QED. Determinants of commuting and anticommuting fields. Coleman-Weinberg effective potential and radiative symmetry breaking. Feynman rules for a generic local field theory. Scalar QED.
5) PERTURBATIVE METHOD AND RENORMALIZABILITY. Brief review of dimensional regularization and Feynman-parameters technique. Higher loop corrections. Locality of ultraviolet divergences. Perturbative renormalizability in diverse dimensions.
6) LAMBDA PHI^3 IN D = 6. Explicit one-loop renormalization. Exact one-loop propagator. Counterterms. Beta function and anomalous dimension. Asymptotic freedom and dimensional transmutation. Two-loop renormalization. Nested and overlapping divergences. Cancellation of non-local divergences.
7) QUANTIZATION OF YM THEORIES. Problems related with the quantization of non abelian gauge fields. Faddeev-Popov method and ghost fields. Independence of the gauge fixing. BRST invariance and physical Hilbert space. Slavnov-Taylor identities.
8) PERTURBATIVE ANALYSIS OF YM THEORIES. Feynman rules. Renormalizability. One loop counterterms and their interrelation. The role of ghosts. Beta function and asymptotic freedom. Lambda QCD. Finiteness of N = 4 Super-YM theories.
9) ANOMALIES. Classical and quantum chiral symmetries. Explicit evaluation of the chiral Schwinger action in two dimensions. ABJ anomalies, triangular graphs and extensions to higher dimensions. Anomalous vertex method. Adler-Bardeen theorem. Anomaly cancellation in the Standard Model. Index theorem.
10) INSTANTONS. Semi-classical solutions in field theory. Instantonic configurations. Theta vacua. The U(1) problem. Wilson-loops.
11) DEEP INELASTIC SCATTERING.
12) AXIOMATIC THEORY. Wightman functions and Schwinger functions. Reconstruction theorem. Triviality of lambda phi^4 theory. Infrared divergences and the problem of charged fields in QED. Goldstone theorem.