Chapter4_17 - PHY4604 R. D. Field Special Unitary 22...

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

View Full Document Right Arrow Icon
PHY4604 R. D. Field Department of Physics Chapter4_17.doc University of Florida Special Unitary 2×2 Matrices Consider the unitary matrix = * * ) , ( a b b a b a U with |a| 2 + |b| 2 = 1 . Such a matrix is said to be “unimodular” since det(U) = |a| 2 + |b| 2 = 1 . Two Component Spinors: This “special” ( i.e. unimodular) unitary 2×2 matrix operates on two component “spinors” = 2 1 ~ v v v as follows = 2 1 * * 2 1 ' ' v v a b b a v v . The transformation leaves the norm of states invariant since > < = + = + + = + = >= < v v v v v v v v v v b a v v v v v v v v | ) ( | | | | ) | | | )(| | | | (| | ' | | ' | ' ' ) ' ' ( ' | ' 2 1 * 2 * 1 2 2 2 1 2 2 2 1 2 2 2 2 2 1 2 1 * 2 * 1 Definition of a Group: A collection of objects is said to form a “group”
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online