Réitigh (igamma_{mu}partial^mu-m)psi=0

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

Réitigh do m.

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

Céimeanna chun Cothromóidí Líneacha a Réiteach

Úsáid an t-airí dáileach chun i\gamma _{μ}∂^{\mu }-m a mhéadú faoi \psi .

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

Bain i\gamma _{μ}∂^{\mu }\psi ón dá thaobh. Is ionann rud ar bith a dhealaítear ó nialas agus a shéanadh.

$$-m\psi =-i\gamma _{μ}∂^{\mu }\psi$$

Tá an chothromóid i bhfoirm chaighdeánach.

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

Roinn an dá thaobh faoi -\psi .

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

Má roinntear é faoi -\psi cuirtear an iolrúchán faoi -\psi ar ceal.

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

Roinn -i\gamma _{μ}∂^{\mu }\psi faoi -\psi .

$$m=i\gamma _{μ}∂^{\mu }$$

Réitigh do γ_μ.

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

Céimeanna chun Cothromóidí Líneacha a Réiteach

Úsáid an t-airí dáileach chun i\gamma _{μ}∂^{\mu }-m a mhéadú faoi \psi .

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

Cuir m\psi leis an dá thaobh. Is ionann rud ar bith móide nialas agus a shuim féin.

$$i\gamma _{μ}∂^{\mu }\psi =m\psi$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$i\psi ∂^{\mu }\gamma _{μ}=m\psi$$

Roinn an dá thaobh faoi i∂^{\mu }\psi .

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

Má roinntear é faoi i∂^{\mu }\psi cuirtear an iolrúchán faoi i∂^{\mu }\psi ar ceal.

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

Roinn m\psi faoi i∂^{\mu }\psi .

$$\gamma _{μ}=-\frac{im}{∂^{\mu }}$$