phys documents (dragged) 78

phys documents (dragged) 78 - 72 Physics Formulary by ir....

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
72 Physics Formulary by ir. J.C.A. Wevers 13.1.4 Isomorfsm and homomorfsm; representations Two groups are isomorphic if they have the same multiplication table. The mapping from group G 1 to G 2 , so that the multiplication table remains the same is a homomorphic mapping. It need not be isomorphic. A representation is a homomorphic mapping of a group to a group of square matrices with the usual matrix multiplication as the combining operation. This is symbolized by Γ . The following holds: Γ ( E )= I I, Γ ( AB )= Γ ( A ) Γ ( B ) , Γ ( A - 1 )=[ Γ ( A )] - 1 For each group there are 3 possibilities for a representation: 1. A faithful representation: all matrices are different. 2. The representation A det ( Γ ( A )) . 3. The identical representation: A 1 . An equivalent representation is obtained by performing an unitary base transformation: Γ ± ( A )= S - 1 Γ ( A ) S . 13.1.5 Reducible and irreducible representations If the same
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/30/2011 for the course PHYSICS 208 taught by Professor Ye during the Spring '10 term at Blinn College.

Ask a homework question - tutors are online