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equations:proca_equation [2018/04/02 13:53]
jakobadmin [Concrete]
equations:proca_equation [2018/04/02 13:53] (current)
jakobadmin [Concrete]
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 The general solution for the Proca equation is The general solution for the Proca equation is
  
-\begin{equation} m^2 A^\rho = \frac{1}{2} ​   \partial_\sigma ( \partial^\sigma A^\rho -  \partial^\rho ​ A^\sigma) \end{equation} 
-is, analogous to the spin $0$ field solution, of the form 
 \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 \\ \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}  ​\label{eq:​aplusminus} &​\equiv ​ A_\mu^+ + A_\mu^- ​  ​\end{align}
equations/proca_equation.txt ยท Last modified: 2018/04/02 13:53 by jakobadmin