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 | | For instance, as opposed to the Proca $4$-vector potentials which transform according to the $(1/2,1/2)$ representation of the Lorentz group, in the $j=1$ case the ``bispinor" functions are constructed via the $(1,0)\oplus (0,1)$ representation what is on an equal footing to the description of Dirac $j=1/2$ particles. |
| | Equations are equivalent (within a constant factor) to the Hammer-Tucker equation~\cite{TUCK1}, see also~\cite{DVOE1,VLAS} \begin{equation}\label{eq:Tucker} (\gamma_{\alpha\beta}p_\alpha p_\beta +p_\alpha p_\alpha +2 m^2) \psi_1 =0 \quad, \end{equation} in the case of the choice $\chi= \vec E +i\vec B$ and $\varphi =\vec E -i\vec B$,\,\,\, $\psi_1 = \mbox{column} (\chi, \quad \varphi)$. |
| | \end{eqnarray} The Weinberg ``bispinor" $(\chi_{\dot\alpha\dot\beta} \quad \varphi^{\alpha\beta})$ corresponds to the equations (\ref{w11}) and (\ref{w21}), meanwhile $(\tilde \chi_{\dot\alpha\dot\beta}\quad \tilde\varphi^{\alpha\beta})$, to the equations (\ref{w1}) and (\ref{w2}). |
| www.ma.utexas.edu /mp_arc/papers/98-106 (7705 words) |
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