Quantum Field Theory: From Basics to Modern Topics

Description

A rigorous and self-contained text reviewing the fundamentals of quantum field theory and exploring advanced topics and modern techniques. Basics of Quantum Field Theory Special relativity Free scalar fields, Mode decomposition Interacting scalar fields LSZ reduction formulas From transition amplitudes to reaction rates Generating functional Perturbative expansion and Feynman rules Calculation of loop integrals Källen-Lehmann spectral representation Ultraviolet divergences and renormalization Spin 1/2 fields Spin 1 fields Abelian gauge invariance, QED Charge conservation, Ward-Takahashi identities Spontaneous symmetry breaking Perturbative unitarity Functional quantization Path integral in quantum mechanics Classical limit, Least action principle More functional machinery Path integral in scalar field theory Functional determinants Quantum effective action Two-particle irreducible effective action Euclidean path integral and Statistical mechanics Path integrals for fermions and photons Grassmann variables Path integral for fermions Path integral for photons Schwinger-Dyson equations Quantum anomalies Non-Abelian gauge symmetry Non-abelian Lie groups and algebras Yang-Mills Lagrangian Non-Abelian gauge theories Spontaneous gauge symmetry breaking theta-term and strong-CP problem Non-local gauge invariant operators Quantization of Yang-Mills theory Introduction Gauge fixing Fadeev-Popov quantization and Ghost fields Feynman rules for non-abelian gauge theories On-shell non-Abelian Ward identities Ghosts and unitarity Renormalization of gauge theories Ultraviolet power counting Symmetries of the quantum effective action Renormalizability Background field method Renormalization group Callan-Symanzik equations Correlators containing composite operators Operator product expansion Example: QCD corrections to weak decays Non-perturbative renormalization group Effective field theories General principles of effective theories Example: Fermi theory of weak decays Standard model as an effective field theory Effective theories in QCD EFT of spontaneous symmetry breaking Quantum anomalies Axial anomalies in a gauge background Generalizations Wess-Zumino consistency conditions 't Hooft anomaly matching Scale anomalies Localized field configurations Domain walls Skyrmions Monopoles Instantons Modern tools for tree level amplitudes Shortcomings of the usual approach Colour ordering of gluonic amplitudes Spinor-helicity formalism Britto-Cachazo-Feng-Witten on-shell recursion Tree-level gravitational amplitudes Cachazo-Svrcek-Witten rules Worldline formalism Worldline representation Quantum electrodynamics Schwinger mechanism Calculation of one-loop amplitudes Lattice field theory Discretization of bosonic actions Fermions Hadron mass determination on the lattice Wilson loops and confinement Gauge fixing on the lattice Lattice worldline formalism Quantum field theory at finite temperature Canonical thermal ensemble Finite-T perturbation theory Large distance effective theories Out-of-equilibrium systems Strong fields and semi-classical methods Introduction Expectation values in a coherent state Quantum field theory with external sources Observables at LO and NLO Green's formulas Mode functions Multi-point correlation functions at tree level