SYMMETRIES in PHYSICS

Symmetry and Groups: Historical Aspects
Symmetry in Physics: A Short History
Group Theory: First Concepts
Abstract Groups - Today’s Formulation
One of the most powerful tools to study transformation properties
and symmetries in physics is the theory of groups.
Definition (Group, CAYLEY)
Abstract elements g ∈ G form a group under the operation ”◦” if:
1 o For any g 1 , g 2 ∈ G the ’product’ g 1 ◦ g 2 ≡ g ∈ G
2 o For any g 1 , g 2 , g 3 ∈ G we have (g 1 ◦ g 2 ) ◦ g 3 = g 1 ◦ (g 2 ◦ g 3 )
3 o There exists a neutral element e ∈ G: ∀ g ∈ G : e ◦ g = g
4 o For any g ∈ G we find inverse g −1 ∈ G such that g ◦ g −1 = e
Jerzy DUDEK
SYMMETRIES in PHYSICS