$ID = get_the_ID();
add_post_meta($ID, 'Author', 'G.Mussardo', True);
add_post_meta($ID, 'Credits', '2', True);
$AUTHOR = get_post_meta(get_the_ID(),'Author',True);
$CREDITS = get_post_meta(get_the_ID(),'Credits',True);
echo "
by $AUTHOR ($CREDITS credits)
“;
?>
Starting and using several examples coming from Physics, the course aims to present the basic properties of one of the most useful and beautiful branches of Mathematics, Group Theory.
Main topics
- Properties
- Representations
- Examples: Platonic Solid, Crystals, Space and Plane Tessellation
- Energy spectrum in periodic and a-periodic systems
- Point Groups
- Permutations: Cayley’s theorem and Young Tableaux
- Potts model and random systems
- Echoes from number theory
- Generators and Commutators
- Baker-Haussdorf formula
- Lie Algebras
- Simple and semi-simple algebras
- The adjoint representation
- Raising and lowering operators
- Irreducible representations
- Coherent states
- Tensor products and 6j-symbols
- Quantum spin chains
- Cold atoms in a two-well trap
- Cartan algebra
- Roots and weights
- Raising and lowering operators
- Structure constants and normalizations
- Positive weights
- Simple roots
- A lot of SU(2)’s groups
- The kaleidoscope of the Weyl group
- The Dynkin diagrams
- Examples from rank 2 algebras:
- 1) SU(3) and eightfold way
- 2) Being exceptional, G2
- Irreducible representations and Young tableaux
- Ising model in a magnetic field, glimpse on E8 structure of nature
- Two famous bosons: Goldstone and Higgs