Are there separate quantum fields for spin 1/2 particles in modern QFT?

[LarryS]

The spin observable for spin 1/2 particles is represented by Pauli Matrices acting upon a 2-dimensional Hilbert Space. In RQM, forgetting about the matter-antimatter duality for the moment, that TWO-state Hilbert Space is directly related, through the Lorentz Group, to the TWO separate differential equations in the Dirac Equation. Is that same "TWO-ness" also found in modern QFT for spin 1/2 particles? Are there TWO separate quantum fields for a spin 1/2 particle in modern QFT? As always, thanks in advance.

 

[atyy]

The Dirac Equation holds in relativistic quantum field theory.

 

[vanhees71]

In addition one cannot stress early enough that a split of angular momentum in an orbital and a spin part is problematic in relativistic quantum field theory (to say the least). A thorough understanding of what's "spin" in relativistic QFT necessarily leads to Wigner's analysis of the irreducible unitary representations of the (quantum version of the) Poincare group. See

Weinberg, S.: The Quantum Theory of Fields, volume 1, Cambridge University Press, 1995

or my QFT lecture notes:

http://fias.uni-frankfurt.de/~hees/publ/lect.pdf

 

[akhmeteli]

It may be relevant to your question that the Dirac equation is generally equivalent to just one (fourth-order) differential equation for just one function. Please see my article http://akhmeteli.org/wp-content/uploads/2011/08/JMAPAQ528082303_1.pdf (JOURNAL OF MATHEMATICAL PHYSICS 52, 082303 (2011)). A derivation in a more general form can be found at http://arxiv.org/abs/1502.02351 .