# L. T. of f(x,t)+g(x,t) = [L.T. f(x,t)]+[L.T. g(x,t)]?

1. Feb 19, 2015

### Spinnor

Suppose I have a pair of solutions of the one dimensional massless complex wave equation in 1+1 dimensional spacetime, solutions with equal and opposite momentum in some rest frame,

Ψ+ = exp[-i(Et+px)]
Ψ- = exp[-i(Et-px)]

Does it matter if

1) I sum Ψ+ and Ψ- and then preform a Lorentz Transformation, or
2) preform the Lorentz Transformation, L.T., on Ψ+ and Ψ- and then sum?

L. T. [f(x,t)+g(x,t)] = [L.T. f(x,t)]+[L.T. g(x,t)] ?

I think the answer is it should not matter the order of operation but I am having trouble simplifying my algebra. Just wondering if there is light at the end of the tunnel.

Thanks for any help!

2. Feb 24, 2015