Symmetry and group theory throughout physics

Group Theory in Particle Physics

1.1 What is a Group? A group is a set of objects with an associated operation which satisfies certain properties. For a group G which is a set of elements {T, T ′, T ′′, ...} with operator ◦, we require: 1. Closure. ∀T, T ′ ∈ G : T ◦ T ′ ∈ G. This property of closure should be familiar to anyone with a linear algebra background, as a vector space also fulfills this property, with addition as th...

Anyons, group theory and planar physics

Relativistic and nonrelativistic anyons are described in a unified formalism by means of the coadjoint orbits of the symmetry groups in the free case as well as when there is an interaction with a constant electromagnetic field. To deal with interactions we introduce the extended Poincaré and Galilei Maxwell groups.

Group representation theory and quantum physics∗

This is a basic tutorial on the use of group representation theory in quantum physics, in particular for such systems as molecules and crystals, which forms the basis of spectroscopic studies in physics and chemistry. Note that, despite the now venerable character of the aforementioned scientific endeavors, group representation theory still finds interesting and novel applications, such as the ...

The Molecular Symmetry Group Theory for Trimethylamine-BH3 Addend(BH3 Free of Rotation)

Applications of Symmetry Methods to the Theory of Plasma Physics

The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal advantage of this “interaction” between plasma physics and symmetry techniques. The examples include, in particular, the complete symmetry analysis of system of two ...