Usually in the first sentence of the definition of the Klein Gordon equation is the statement that it describes spin-0 particles.(adsbygoogle = window.adsbygoogle || []).push({});

Similarly, in the first sentence of the definition of the Dirac equation is the statement that it describes spin-1/2 particles.

But then comes the bit that got me to write this post -- a few sentences later in that latter definition, you're bound to run into the fact that the Dirac equation is the formal square root of the Klein-Gordon equation, and that therefore any solution to the Dirac equation is also solution of the Klein-Gordon equation (though obviously not vice-versa; [itex]x = y \rightarrow x^{2} = y^{2}[/itex], but [itex]x^{2} = y^{2} !\rightarrow x = y[/itex]).

So...what gives? How can you say that "the Klein-Gordon equation describes spin-0 particles" when every spin-1/2 particle (or at least all of those described by the Dirac equation) is also a solution?

Looking at the Klein-Gordon equation, it seems like it should be valid for *any* relativistic particle -- [itex]E^{2} = p^{2} + m^{2}[/itex] is generally true, right?

My gut is telling me that the answer is that while the Klein-Gordon has many non-scalar-particle solutions, it only provides a *complete* description of spin-0 particles...but that seems like a big enough distinction to warrant at least an asterisk in that ever-present first sentence.

Also, feel free to school me on spin, field quantization, or anything else that I obviously have only a really shallow understanding of.

Thanks,

Justin

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# Klein-Gordon field is spin-0: really?

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