Saturday, September 10, 2016

special relativity - Klein gordon field and positive/negative energy solutions


I my course we calculated the Klein-Gordon field:


$$ \phi(x)= \int \frac{d^3k}{(2 \pi)^3}\frac{1}{2k_0} ~ \left[a(\vec{k})e^{-ik.x}+b^*(\vec{k})e^{i kx}\right]$$


We said that the part $ a(\vec{k})e^{-ikx} $ correspond to the positive energies solutions, and the part $b^*(\vec{k})e^{i kx}$ to the negative ones. (We are not doing quantum mechanics here, $a(\vec{k})$ and $b^*(\vec{k})$ are numbers).


Why do we say this?




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