Quantum Field Theory

Recommended Prerequisites

Relativistic Quantum Mechanics.

Teaching Methods

Expositive teaching with constant references to physical systems whose description fits the equations presented. Emphasis will be given to the mathematical techniques needed to obtain the properties of the dispersion and production processes in the field of elementary particle physics.

Learning Outcomes

Recognize the importance of non-perturbative methods for data analysis regarding the dispersion and particle production in high energy processes, both in particle accelerators, such as LHC, DESY, Fermilab BEPC and KEK, or in experiments with cosmic rays, as the Pierre Auger cosmic Ray Observatory.

Knowing the Bethe-Salpeter and the Schwinger-Dyson equations.

Knowing how to calculate cross sections of processes involving weak, strong and electromagnetic interactions.

Work Placement(s)

No

Syllabus

Lagrangean densities, symmetries and conservation laws.
Klein-Gordon and Dirac fields: second quantisation; commutation  and anti commutation relations between creation and annihilation operators. Propagators.
Quantisation of the electromagnetic field.
S-matrix formalism.
Feynman diagrams and their rules in QED (Quantum Electrodynamics).
Regularisation methods.

Head Lecturer(s)

Maria Constança Mendes Pinheiro da Providência Santarém e Costa

Assessment Methods

Assessment
Exam: 100.0%

Bibliography

-Michael Peskin, Daniel Schroeder, An Introduction to Quantum Field Theory, Westview Press
-J. Bjorken, S. Drell, Relativistic Quantum Fields, McGraw-Hill
-Eef van Beveren, Some notes on Field Theory.
-R. J. Rivers, Path integral methods in quantum field theory, Cambridge University Press, 1987.
-Ta-Pei Cheng and Ling-Fong Li, Gauge theory of elementary particles, Clarendon Press, 1984.
-C. D. Roberts and A. G. Williams, Dyson-Schwinger equations and their application to hadronic physics, Prog. Part. Nucl. Phys.  33, 477 (1994).
-C. D. Roberts, Hadron Properties and Dyson-Schwinger Equations, Prog. Part. Nucl. Phys.  61, 50 (2008).
-M. S. Bhagwat, A. Hoell, A. Krassnigg, C. D. Roberts and S. V. Wright, Schwinger functions and light-quark bound states, Few Body Syst.  40, 209 (2007).
-A. Krassnigg, C. D. Roberts and S. V. Wright, Meson spectroscopy and properties using Dyson-Schwinger equations, Int. J. Mod. Phys.  A22, 424 (2007).