Advanced Field Theory

Recommended Prerequisites

Relativistic Quantum Mechanics, Quantum Field Theory.

Teaching Methods

Expository teaching with constant references to physical systems whose description fits the equations presented. Emphasis will be given to the mathematical techniques necessary to obtain the properties of the dispersion and production of elementary particles.

Learning Outcomes

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

- To know the Bethe-Salpeter and the Schwinger-Dyson equations.

- Calculate Cross sections of processes involving strong and electro-weak interactions.

Work Placement(s)

No

Syllabus

- Feynman diagrams Feynman through the path integral method and review of perturba-tive methods.

- The lagrangian density of the Standard Model.

- The Bethe-Salpeter equation and its three dimensional reductions.

- Schwinger-Dyson diagrams.

- Applications: Dispersion and production of hadrons, processes involving gauge bosons and Higgs particles, dressed quark propagators, bound states of quarks, hadronic spectroscopy .

Head Lecturer(s)

Pedro Almeida Vieira Alberto

Assessment Methods

Assessment
Research work: 50.0%
Exam: 50.0%

Bibliography

-R. Blankenbecler and R. Sugar,Linear integral equations for relativistic multichannel scattering,Phys. Rev. 142,
1051 (1966).
-A. A. Logunov and A. N. Tavkhelidze,Quasioptical approach in quantum field theory,Nuovo Cim. 29, 380 (1963).
-E. D. Cooper and B. K. Jennings,Obtaining the one-body limit from the relativistic two-body equation,Nucl. Phys.
A500, 553 (1989).
-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,Mes