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Describing relativistic fermions with two-component field

YU-Qi Chen
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Abstract

With a non-unitary transformation, the Lagrangian of a Dirac fermion is decomposed into two decoupled sectors. We propose to describe massive relativistic fermions in gauge theories in a two-component form. All relations between the Green's functions in this form and those in the conventional four-component form are derived. It is shown that the S-matrix elements in both forms are exactly the same. The description of the fermion in the new form simplifies significantly the gamma-matrix algebra in the four-component form. In particular, in perturbative calculations the propagator of the fermion is a scalar function. The advantages of the two-component form make it very useful in practical applications.

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YU-Qi Chen. 2004-09-03. Describing relativistic fermions with two-component field. https://arxiv.org/abs/hep-ph/0409027

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