Lie Groups and Quantum Chromodynamics

Lie Groups and Quantum Mechanics

Mathematical modeling should present a consistent description of physical phenomena. We illustrate an inconsistency with two Hamiltonians – the standard Hamiltonian and an example found in Goldstein – for the simple harmonic oscillator and its quantisation. Both descriptions are rich in Lie point symmetries and so one can calculate many Jacobi Last Multipliers and therefore Lagrangians. The Las...

Algebraic methods: Lie groups, quantum groups

These notes concentrate on the paradigm of spherical functions on Riemannian symmetric spaces. This paradigm has led to the notion of special functions associated with root systems. The first sections deal with older work on the interaction between spherical functions on rank one symmetric spaces and special functions (q=1) in one variable. The (spectacular) developments in the higher rank case...

Quantum Algebras and Lie Groups A

Quantum groups are born in Leningrad[1] in connection with the quantum inverse problem method as it arises in soliton theory. Other motivations came out after and the logic of the subject has been repeatedly reversed[2] and it is still not univocally established. The approach followed here attempts to use the link of the field with Lie groups as much as it is possible at the moment and, perhaps...

Poisson Lie groups and their relation to quantum groups

Quantum Chromodynamics

After a brief historical review of the emergence of QCD as the quantum field theory of strong interactions, the basic notions of colour and gauge invariance are introduced leading to the QCD Lagrangian. The second lecture is devoted to perturbative QCD, from tree-level processes to higher-order corrections in renormalized perturbation theory, including jet production in e + e − annihilation , h...