Spin 1 Spinor Construction with Clifford Algera and Dirac Spin 1/2 Spinors

Abstract

A compatible spin 1 spinor representation with Clifford algebra (1,3) (or 1,3 Cl ) is derived for both (1 / 2,1 / 2) and (1, 0) (0,1)  Lorentz group representations with spin 1/2 particles Dirac spinors in 1,3 Cl . The relation between the two different representations of spin 1 spinors is analogous to the relation between the electromagnetic vector potential field A and the electromagnetic field strength tensor F  . From this relationship, the two representations are combined by the formula u( p, )  ( p, )  p / m. We also note that the Grassmann basis provides more convenient basis for spin 1 spinors especially in chiral representations of (1, 0) (0,1)  , even though the Clifford basis is more fitting for spin 1/2 and (1/ 2,1/ 2) spinor representations for both helicity and handedness.

Keywords

• Clifford Algebra
• Spinors
• Spin

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