Negative energy solutions in Klein Gordon and Dirac equations It is often read that Dirac equation poses the problem of negative energy solutions (later solved by antiparticles and second quantization/QFT schema). My question is: negative energy solutions were obviously present also in the previous KG equation. Why they were not considered a problem? I read somewhere that this was related to the second order derivative in KG but it is not entirely clear to me.
 A: In QFT, when making a field operator, negative frequency solutions correspond to annihilation operators while positive frequency solutions correspond to creation operators. Not worrying about normalizations and things like that,
$$
\hat \phi(x) \propto \int d^3 k \left( \hat a(k) e^{- i k \cdot x} + \hat a^\dagger(k) e^{ i k \cdot x} \right).
$$
Furthermore, Dirac's initial worry, that the Klein Gordon current isn't positive definite, was really a misconception stemming from the fact that people didn't understand how to quantize spin $0$ particles at the time. It is only the negative frequency solutions which have a negative  probability current, but those don't correspond to the probability current of actual particle states. Only positive frequency solutions, i.e. particles created on the vacuum, have probability currents which are indeed positive.
Dirac's initial interpretation was that special relativity required particles to have spin, but really this was just because there was a lot of confusion over how to interpret the different mathematical objects in QFT. There are certainly particles without spin, like the Higgs boson for instance.
