PH-703   Quantum Field Theory II

1. Non-abelian gauge theories: Yang-Mills Lagrangian, local and global gauge transformation. Multiple vacua.
2. Brief review of group theory, quantization of non-abelian gauge theories, ghost field (BRS transformations).
3. Unitarity: ghost field and unitarity, optical theorem and Cutkosky rules, examples: e + e → hadrons (evidence of color).
4. Radiative corrections in QCD: one loop divergences (gauge boson self-energy, fermion self-energy), fermion gluon vertices, beta function and asymptotic freedom.
5. Callan-Symanzik equation: renormalization scale, methods of characteristics, examples in φ4 theory and QCD.
6. Weak interactions and Fermi theory: spontaneous symmetry breaking, massive gauge bosons (Higgs mechanism), Goldstone theorem with application to pi-sigma lagrangian, Goldstone bosons.
7. Electroweak unification: Gauge theory with spontaneous symmetry breaking, neutral and charged currents, radiative corrections from fermionic loops, Higgs couplings, Higgs contribution to vector boson self energy, calculation: top quark decay into (i) W + b (ii) φ+ b, Higgs decay into: (i) W+W (ii) φ + W (iii) φ + φ, Yang Mills character of W-bosons (triple tri-linear coupling), triangle anomaly.
8. Multiple vacua in QCD and the strong CP problem.

Recommended texts:

• An Introduction to Quantum Field Theory, M.E.Peskin and D.V.Schroeder,  1995.
• Quantum Field Theory, F. Mandl and G. Shaw,  (Wiley, 1993).
• Quantum Field Theory in a Nutshell, A. Zee,  (Princeton University Press, 2003).
• Quantum Field Theory, M. Srednicki , (Cambridge University Press, 2007)