Special unitary group
In abstract algebra, the special unitary group of degree n over a field F (written as SU(n,F)) is the group of n by n unitary matrices with determinant 1 and entries from F, with the group operation that of matrix multiplication. This is a subgroup of the unitary group U(n,F), itself a subgroup of the general linear group Gl(n,F).If the field F is the field of real or complex numbers, then the special unitary group SU(n,F) is a Lie group.
A common matrix representation of the generatorss of SU(2) is:
is the square root of -1.)
This representation is often used in quantum mechanics to represent the spin of fundamental particles such as electrons. They also serve as unit vectors for the description of our 3 spatial dimensions in quantum relativity.Note that the product of any two different generators is another generator, and that the generators anticommute. Together with the identity matrix,
