Zero-mass limit of a Dirac spinor with general spin orientation

Abstract

The helicity eigenstates that describe fermions with a special spin orientation (parallel or antiparallel to the direction of momentum) provide a considerable simplification in calculations. Hence, it is generally preferred to use the helicity basis during calculations in relativistic quantum mechanics or the quantum field theory. Possibly for the above reason, Dirac spinors describing a general spin orientation have been ignored in many textbooks. Although the helicity eigenstates give an almost complete understanding of the behavior of the free Dirac solutions, the zero-mass limit is one of its exceptions. The zero-mass behavior of the free spinor with general spin orientation and its relation with chirality eigenstates has been skipped in textbooks and hence it deserves a clear, detailed investigation. In this paper we obtain the free Dirac spinors describing a general spin orientation and examine their zero-mass limit. We also briefly discuss some of the implications of this small-mass behavior of the spinors on particle physics.