Einstein Summation Convention / Lorentz "boost"

[mathtrek]

I'm struggling with understanding the Einstein Summation Convention with respect to Lorentz transformations. Is anybody able to point me in the direction of some easy to read resources on the subject? Thanks in advance!

[Severian]

I presume your difficulty is coming from the indices being up or down.

 

If it disturbs you, you can really avoid it. Regard all vecors (index up) as being standard column vectors and all co-vectors (index down as representing a column vector premultied by a matrix, the metric (i.e. a dagonal matric with diagonal entries 1, -1, -1, -1), e.g. [math]x_\mu = g_{\mu \nu} x^\nu[/math]. Then all indices are up (except for the matric) and you can explicitly write in the sum over repeated indices.

 

That procedure makes the algebra look exactly like matrix algebra, so should be more familiar.