Twisted photons with finite orbital angular momentum have a distinct mode profile topological charge at the center of while propagating in certain direction. Each different charges m is orthogonal, sense that overlap integral vanishes among modes values . Here, we theoretically consider superposition state three left and right vortices Gaussian without vortex. These states are considered to be ...

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...

The classical Lagrangian of chromodynamics, its quantization in the perturbation theory framework, and renormalization form the subject of these lectures. Symmetries of the theory are discussed. The dependence of the coupling constant αs on the renormalization scale μ is considered in detail.

These lectures on QCD stress the theoretical elements that underlie a wide range of phenomenological studies, particularly gauge invariance, renormalization, factorization and infrared safety. The three parts cover the basics of QCD, QCD at tree level and higher order corrections. Lectures given at the 2004 European School of High-Energy Physics, St. Feliu de Guı́xols, Barcelona, Spain, 30 May –...