Group Theory: Mathematical Expression of Symmetry in 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...

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

Selected topics in Mathematical Physics: Quantum Information Theory Talk 5: Averages over the unitary group

In this talk, it is shown how to calculate averages over the Unitary group by applying mathematical tools presented in the previous talk. Particulary, Schur’s Lemma is utilized to two useful examples. Eventually, the results are used to show that a random pure state on a finite-dimensional bipartite Hilbert space is close to maximally entangled. 1 Representations of the Unitary group and Schur’...

A mathematical theory of isolated systems in relativistic plasma physics

The existence and the properties of isolated solutions to the relativistic Vlasov-Maxwell system with initial data on the backward hyperboloid t=− √ 1+ |x| are investigated. Isolated solutions of Vlasov-Maxwell can be defined by the condition that the particle density is compactly supported on the initial hyperboloid and by imposing the absence of incoming radiation on the electromagnetic field...

Some Problems in the Theory of Dynamical Systems & Mathematical Physics *