A. Zee, Quantum Field Theory in a Nutshell · Problem II.3.4

Field Theory Redux

Physics — QFT

Problem

Show that a spin 32\frac{3}{2} particle can be described by a vector-spinor Ψαμ\Psi_{\alpha\mu}, namely a Dirac spinor carrying a Lorentz index. Find the corresponding equations of motion, known as the Rarita-Schwinger equations. [Hint: The object Ψαμ\Psi_{\alpha\mu} has 16 components, which we need to cut down to 2⋅32+1=42 \cdot \frac{3}{2} + 1 = 4 components.]

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