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Lie Groups, Lie Algebras, Gauge Theories and Standard Model

Lie Groups, Lie Algebras, Gauge Theories and Standard Model

Code	13327
Year	1
Semester	S2
ECTS Credits	10
Workload	OT(30H)/TP(30H)
Scientific area	Física e Matemática
Entry requirements	No.
Learning outcomes	This UC aims to provide students with a working knowledge of Lie groups and algebras and gauge theories in general, and the Standard Model and important current research paths for its necessary extension. The approach is designed to prepare students to develop research papers on models and phenomenology of High Energy Physics. At the end of this UC the student should: - know Lie groups and algebras, with an emphasis on their most relevant representations for gauge theories; - understand the construction, quantization and tools for calculating non-abelian gauge theories with spontaneous symmetry breaking; - know the Standard Model and its phenomenology; - understand the need to go beyond the Standard Model and some of the most important directions of research; - be able to tackle problems, deepen knowledge and explore the literature independently.
Syllabus	1. Lie groups and Lie algebras Lie groups Representation of Lie groups. Representation of compact Lie groups Lie algebras. Relationship between algebra and group properties The Poincaré Group. Classification of representations. Dirac's equation. Simple Lie Algebras. Roots and Weights. Dynkin diagrams. Classification and representations Tensorial methods. Unreducible representations of SU (n). Young Tableaux. 2. Gauge Theories. U (1) Gauge symmetry and QED Non-abelian gauge symmetry. Yang-Mills Theory Spontaneous symmetry breaking. Higgs Mechanism Quantization by path integral. Faddeev - Popov ansatz. Feynman rules on renormalizable gauges BRST Symmetry Renormalization 3. The Standard Model Standard Model Fields and Symmetries QCD Electroweak theory Standard Phenomenology 4. Beyond the Standard Model Physics of neutrinos Great Unification Supersymmetry
Main Bibliography	ES Abers, BW Lee 1973 Gauge Theories (Physics Reports 9, No. 1, 1-141) RN Cahn 1984 Semi-Simple Lie Algebras and their Representations, Benjamin Cummings A Das, S Okubo 2014 Lie Groups and Lie Algebras for Physicists, World Scientific PH Frampton 2008 Gauge Field Theories 3ed, Wiley H Georgi 1999 Lie Algebras in Particle Physics: From Isospin to Unified Theories 2ed, Westview Press BC Hall 2015 Lie Groups, Lie Algebras, and Representations: An Elementary Introduction 2ed, Springer P Langacker 2017 The Standard Model and Beyond 2ed, CRC Press ME Peskin, DV Schroeder 1995 An Introduction to Quantum Field Theory, Perseus Books P Ramond 2001 Field Theory: A Modern Primer 2ed, Westview Press A Zee 2010 Quantum Field Theory in a Nutshell 2ed, Princeton Univ.Press A Zee 2016 Group Theory in a Nutshell for Physicists, Princeton Univ.Press
Language	Portuguese. Tutorial support is available in English.