Introduction to Quantum Field Theory

1. Review of classical field theory; 2. Quantum mechanics; 3. Canonical quantization of scalar fields; 4. Propagators for free scalar fields; 5. Interaction picture and wick theorem for phi4 in operator formalism; 6. Feynman rules for phi4 from the operator formalism; 7. The driven (forced) harmonic oscillator; 8. Euclidean formulation and finite temperature field theory; 9. The Feynman path integral for a scalar field; 10. Wick theorem for path integrals and Feynman rules part I; 11. Feynman rules in X-Space and P-Space; 12. Quantization of the Dirac field and Fermionic path integral; 13. Wick theorem, Gaussian integration and Feynman rules for fermions; 14. Spin sums, Dirac field bilinears and C,P,T symmetries for fermions; 15. Dirac quantization of constrained systems; 16. Quantization of gauge fields, their path integral, and the photon propagator; 17. Generating functional for connected Green's Functions and the effective action (1PI Diagrams); 18. Dyson-Schwinger equations and ward identities; 19. Cross sections and the S-Matrix; 20. The S-matrix and Feynman diagrams; 21. The optical theorem and the cutting rules; 22. Unitarity and the largest time equation; 23. QED; 24. Nonrelativistic processes; 25. E+E- L¯ L unpolarized cross section; 26. E+E- L¯ L polarized cross section; 27. (Unpolarized) Compton scattering; 28. The Helicity Spinor formalism; 29. Gluon amplitudes, the Parke-Taylor formula and the BCFW construction; 30. Review of path integral and operator formalism and the Feynman diagram expansion; 31. One-loop determinants, vacuum energy and zeta function regularization; 32. One-loop divergences for scalars; 33. Regularization, definitions; 34. One-loop renormalization for scalars and counterterms in dimensional regularization; 35. Renormalization conditions and the renormalization group; 36. One-loop renormalizability in QED; 37. Physical applications of one-loop results 1. Vacuum Polarization; 38. Physical applications of one-loop results 2. Anomalous

Nastase, Horatiu Hora iu Nastase is a Researcher at the Institute for Theoretical Physics at the Universidade Estadual Paulista, São Paulo. To date, his career has spanned four continents. As an undergraduate he studied at the Universitatea din Bucure ti and Københavns Universitet. He later completed his Ph.D. at the State University of New York, Stony Brook, before moving to the Institute for Advanced Study, Princeton University, New Jersey, where his collaboration with David Berenstein and Juan Maldacena defined the pp-wave correspondence. He has also held research and teaching positions at Brown University, Rhode Island and the Tokyo Institute of Technology. His other books include Introduction to the AdS/CFT Correspondence (Cambridge, 2015), String Theory Methods for Condensed Matter Physics (Cambridge, 2017) and Classical Field Theory (Cambridge, 2019).