Hello I am trying to work out the Casimir force via the Abel-Plana equation. I have been following the derivation in http://arxiv.org/abs/quant-ph/0106045. Specifically I can't figure out for the life of me how the author is going from the first part of equation 2.33 to the second part of it. I am trying to figure out if it something simple I am just over looking. In my calculations the last term of the first equality has a 1/2 that refuses to go away. This prevents regularization using the Abel-Plana equation. The only way I can see around it, is to assume the integration over dk3 goes from -infinity to infinity and convert that to twice the integral of 0 to infinity. In which case one has to ask how does negative wave numbers make any sense? I am typing this really late as I have spent all day on this, I will try to put up some equations tomorrow if I have time. But everything that is relevant is in the arXiv paper.