Syllabus
* 1. Gauge invariance.
Electromagnetic fields, U(1) gauge transformations. Yang-Mills fields, non-abelian gauge group, parallel transport, covariant derivative, intensity tensor, Wilson loop. Invariant Lagrangians, scalar and spinor fields.
* 2. Classical solutions
Equations of motion, Bianchi identities. Hamilton formalism, Gauss law. Classical solutions in Minkowski regime, (non)existence of soliton solutions. Classical solutions in the Euclidean regime, instantons.
* 3. Quantization of gauge fields
Hamiltonian systems with constraints, Dirac quantization. Functional integral, gauge fixation, Faddeev-Popov ghosts, Feynman rules. BRST symmetry. Batalin-Vilkovisky method.
* 4. Renormalization of gauge theories
UV divergences, regularization, renormalization. Renormalizability of gauge theories, anomalies. Renormalization group, asymptotic freedom.
* 5. Spontaneous gauge symmetry breaking
Spontaneous global symmetry breaking, Goldstone theorem. Spontaneous local symmetry breaking, Higgs mechanism. Dynamical gauge symmetry breaking.
* 6. Gauge theories in particle physics
Quantum chromodynamics. The Standard Model of electroweak interactions. Grand unification theory.
Annotation
Gauge invariance, quantization of gauge fields, renormalization and renormalization group, spontaneous symmetry breaking, gauge theories in particle physics, the standard model. For the 2nd year of the Thoeretical
Physics and Particle and Nuclear Physics studies and postgraduate students.