Complex analysis
Multivalued functions, cuts, notion of Riemann surface. Theorem of residues, and applications. Analytic continuation, with examples. Special functions: Gamma an Zeta functions, Hypergeometic function, Fuchsian Equations. Elliptic functions. Simple asymptotic methods. Saddle-point Method.
Lie algebras and groups
Lie algebras and groups. Linear representations. Classification of semisimple Lie algebras and Dynkin diagrams. Differential geometry of Lie groups.
The textbooks will be suggested according to the different subjects to be treated.
Learning Objectives
Knowledge acquired:
As specified in the contents of the course contents.
Competence acquired :
Possibility of understanding the basics of modern physical theories, both in their foundational and technical aspects.
Skills acquired (at the end of the course):
The student must assimilate basic concepts of the course and master the involved techniques, like asymptotic expansions, tensor product and reduction of group representations.
Teaching Methods
6 CFU
Lectures hours: 48
Further information
The first part of the course is taught by F. Colomo, the second one by F. Bonechi.
Office hours:
on demand,
bonechi@fi.infn.it
colomo@fi.infn.it
Website: http://theory.fi.infn.it/colomo
Type of Assessment
Written exercises and oral examination
Course program
Complex analysis
Multivalued functions, cuts, notion of Riemann surface. Theorem of residues, and applications. Analytic continuation, with examples. Special functions: Gamma an Zeta functions, Hypergeometic function, Fuchsian Equations. Elliptic functions. Simple asymptotic methods. Saddle-point Method.
Lie algebras and groups
Lie algebras and groups. Linear representations. Classification of semisimple Lie algebras and Dynkin diagrams. Differential geometry of Lie groups.