- you can write your equation with use only
align*
environment
- equation is wider than text width, consequently it spill out from right text border:

(red lines indicate page layout)
\documentclass{extarticle}
\usepackage{amsmath}
%---------------- show page layout. don't use in a real document!
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.15pt}
\renewcommand*\ShowFrameColor{\color{red}}
%---------------------------------------------------------------%
\begin{document}
\begin{align*}
U(x)
& = e^{i\theta^a(x)T^a} & U(x) & = e^{-\theta^a(x)(t_a)^i{}_j} \\
[T^a,T^b]
& = if^{abc}T^c & [t^a,t^b] & = f_{ab}{}^c t^c \\
\delta\phi_i
& = i\theta^a(T^a)_{ij}\phi_j &
\delta \phi^i & = -\theta^a(t_a)^i{}_j \phi^j \\
&& & = -\theta^af_{aj}{}^i \phi^j \\
&& & = \theta^af_{ja}{}^i \phi^j \\
A_\mu
& = A_\mu{}^a T^a &
A_\mu &= A_\mu{}^a t_a \\
A_\mu
& \rightarrow U(x) A_\mu U(x)^{-1} - \frac{i}{g} [\partial_\mu U(x)] U(x)^{-1} &
A_\mu & \rightarrow U(x) A_\mu U(x)^{-1}
- \frac{1}{g} [\partial_\mu U(x)] U(x)^{-1}
\end{align*}
\end{document}
- this problem you can solve on two ways, for example:
- enlarge text area for example with use of the `geometry package
- break last equation in each column

\documentclass{extarticle}
\usepackage{amsmath}
%---------------- show page layout. don't use in a real document!
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.15pt}
\renewcommand*\ShowFrameColor{\color{red}}
%---------------------------------------------------------------%
\begin{document}
\begin{align*}
U(x)
& = e^{i\theta^a(x)T^a} & U(x) & = e^{-\theta^a(x)(t_a)^i{}_j} \\
[T^a,T^b]
& = if^{abc}T^c & [t^a,t^b] & = f_{ab}{}^c t^c \\
\delta\phi_i
& = i\theta^a(T^a)_{ij}\phi_j &
\delta \phi^i & = -\theta^a(t_a)^i{}_j \phi^j
= -\theta^af_{aj}{}^i \phi^j \\
&& & = \theta^af_{ja}{}^i \phi^j \\
A_\mu
& = A_\mu{}^a T^a &
A_\mu &= A_\mu{}^a t_a \\
A_\mu
& \rightarrow U(x) A_\mu U(x)^{-1} &
A_\mu & \rightarrow U(x) A_\mu U(x)^{-1} \\
&\qquad - \frac{i}{g} [\partial_\mu U(x)] U(x)^{-1} &
&\qquad - \frac{1}{g} [\partial_\mu U(x)] U(x)^{-1}
\end{align*}
\end{document}