Whakaoti i te (igamma_{mu}partial^mu-m)psi=0

$$( i \gamma _ { \mu } \partial ^ { \mu } - m ) \psi = 0$$

Whakaoti mō m

$$\left\{\begin{matrix}\\m=i\gamma _{μ}∂^{\mu }\text{, }&\text{unconditionally}\\m\in \mathrm{C}\text{, }&\psi =0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te i\gamma _{μ}∂^{\mu }-m ki te \psi .

$$i\gamma _{μ}∂^{\mu }\psi -m\psi =0$$

Tangohia te i\gamma _{μ}∂^{\mu }\psi mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-m\psi =-i\gamma _{μ}∂^{\mu }\psi$$

He hanga arowhānui tō te whārite.

$$\left(-\psi \right)m=-i\gamma _{μ}\psi ∂^{\mu }$$

Whakawehea ngā taha e rua ki te -\psi .

$$\frac{\left(-\psi \right)m}{-\psi }=-\frac{i\gamma _{μ}\psi ∂^{\mu }}{-\psi }$$

Mā te whakawehe ki te -\psi ka wetekia te whakareanga ki te -\psi .

$$m=-\frac{i\gamma _{μ}\psi ∂^{\mu }}{-\psi }$$

Whakawehe -i\gamma _{μ}∂^{\mu }\psi ki te -\psi .

$$m=i\gamma _{μ}∂^{\mu }$$

Whakaoti mō γ_μ

$$\left\{\begin{matrix}\gamma _{μ}=-\frac{im}{∂^{\mu }}\text{, }&\mu =0\text{ or }∂\neq 0\\\gamma _{μ}\in \mathrm{C}\text{, }&\psi =0\text{ or }\left(m=0\text{ and }∂=0\text{ and }\mu \neq 0\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te i\gamma _{μ}∂^{\mu }-m ki te \psi .

$$i\gamma _{μ}∂^{\mu }\psi -m\psi =0$$

Me tāpiri te m\psi ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$i\gamma _{μ}∂^{\mu }\psi =m\psi$$

He hanga arowhānui tō te whārite.

$$i\psi ∂^{\mu }\gamma _{μ}=m\psi$$

Whakawehea ngā taha e rua ki te i∂^{\mu }\psi .

$$\frac{i\psi ∂^{\mu }\gamma _{μ}}{i\psi ∂^{\mu }}=\frac{m\psi }{i\psi ∂^{\mu }}$$

Mā te whakawehe ki te i∂^{\mu }\psi ka wetekia te whakareanga ki te i∂^{\mu }\psi .

$$\gamma _{μ}=\frac{m\psi }{i\psi ∂^{\mu }}$$

Whakawehe m\psi ki te i∂^{\mu }\psi .

$$\gamma _{μ}=-\frac{im}{∂^{\mu }}$$