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equations:proca_equation [2018/03/28 10:24] jakobadmin |
equations:proca_equation [2018/04/02 13:53] jakobadmin [Concrete] |
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&=\partial_\sigma F^{\sigma \rho} | &=\partial_\sigma F^{\sigma \rho} | ||
\end{align} | \end{align} | ||
- | + | ||
+ | |||
+ | The general solution for the Proca equation is | ||
+ | |||
+ | \begin{align} A_\mu &= \int \frac{d^3 k}{\sqrt{ (2\pi)^3 2 \omega_k}} \left( \epsilon_{r,\mu}(k) a_r(k) {\mathrm{e}}^{-ikx} + \epsilon_{r,\mu}(k) a_r^\dagger(k) {\mathrm{e}}^{ikx} \right) \notag \\ | ||
+ | \label{eq:aplusminus} &\equiv A_\mu^+ + A_\mu^- \end{align} | ||
+ | where $\epsilon_{r,\mu}(k)$ are basis vectors called polarization vectors. | ||
<tabbox Abstract> | <tabbox Abstract> | ||