Meaning of terms in SU(3) gauge transformation

[neorich]

Hi All,

I'm working through the theory of the strong interaction and I roughly follow it. However I have some questions about the meaning of the terms.

The book I use gives the gauge transformation as: $\psi \rightarrow e^{i \lambda . a(x)} \psi$

First question ... What are the $a(x)$ terms. My book tells me they are real numbers, but that begs two further questions ... if they are real numbers, then what do they represent? And if they are real numbers then the product $\lambda.a(x)$ is a matrix since the $\lambda$s are matrices, so we have the exponential function raised to the power of a matrix? What does this mean?

Thank for any help provided

Regards

neorich

 

[bapowell]

Try this:

http://en.wikipedia.org/wiki/Matrix_exponential