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  Why is it legitimate using bispinors in HQET?

+ 3 like - 0 dislike

I am reading about HQET in Grozin's book http://www.amazon.es/Effective-Theory-Springer-Tracts-Physics/dp/3540206922. While constructing the Lagrangian he first consider the usual QCD Lagrangian with only one heavy quark and many lights. He then says that if we consider characteristic momenta of the heavy quark smaller than its mass we cann simplify the energy momentum dispersion relation to 


and that as a result the bilinear part of the heavy quark Lagrangian can be taken to be 


he then states that we can use two component spinors to describe spin instead of four component ones. Can somebody give me a justification for this last step? don't we lose degrees of freedom this way?

asked Jan 16, 2016 in Theoretical Physics by Dmitry hand me the Kalashnikov (735 points) [ no revision ]

Spin is always 1/2 and is always described with two-component spinors. Four-component spinors include states of anti-particle with spin 1/2. In a low-momentum region the antiparticle amplitude is much smaller than the particle one (or vise versa), so one two-component spinor for one (anti) particle suffices.

@VladimirKalitvianski: You'd post this as an answer (with vice in place of wise). It tells everything.

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