- #1
arroy_0205
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I have some doubts regarding SU(3). These are at very basic level.
First, how does one construct adjoint representation of SU(3)? What will be the dimensionality of the matrices? The defining matrices in terms of Gell-Mann matrices are 3x3 but in the case of adjoint representation the matrices have to satisfy the condition:
[tex]
[T_a]_{bc}=-if_{abc}
[/tex]
and we know f_{147} etc are nonzero so in this case, b=4, c=7. Is this right?
Second: In the book "Lie algebras in Particle Physics", H. Georgi gives (p101, equation no 7.12) the forms of [tex]E_{\pm1,0}[/tex] etc for SU(3). I do not understand how these generators are calculated. Can anybody please help?
First, how does one construct adjoint representation of SU(3)? What will be the dimensionality of the matrices? The defining matrices in terms of Gell-Mann matrices are 3x3 but in the case of adjoint representation the matrices have to satisfy the condition:
[tex]
[T_a]_{bc}=-if_{abc}
[/tex]
and we know f_{147} etc are nonzero so in this case, b=4, c=7. Is this right?
Second: In the book "Lie algebras in Particle Physics", H. Georgi gives (p101, equation no 7.12) the forms of [tex]E_{\pm1,0}[/tex] etc for SU(3). I do not understand how these generators are calculated. Can anybody please help?