Università Roma Tre

Group Theory (CA)

SU(2) and SU(3)

The Killing Form

Simple Lie Algebras

Representations

Simple Roots and the Cartan Matrix

The Classical Lie Algebras

The Exceptional Lie Algebras

Casimir Operators and Freudenthal’s Formula

The Weyl Group

Weyl’s Dimension Formula

Reducing Product Representations

Subalgebras

Branching Rules

Numerical Methods

Refresh on Probability and Random variables

Refresh on Measurement, uncertainty and its propagation

Refresh on Curve-fitting, least-squares, optimization

Classical numerical integration, speed of convergence

Integration MC (Mean, variance)

Sampling Strategies

Applications

Propagation of uncertainties

Generation according to a distribution


Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html

Robert Cahn - Semi-Simple Lie Algebras and Their Representations - Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )

Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269

Taylor, J. - An introduction to error analysis - University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre

Dubi, A. - Monte Carlo applications in systems engineering - Wiley Disponibile nella biblioteca Scientifica di Roma Tre

readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html