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Lagrangian formalism for the Dirac equation including charge

What is Dirac Lagrangian?
In summary, the Dirac Lagrangian has an equation of motion that is either the Dirac equation or a [overline]Ψ[\\overline] version of the Dirac equation.
The first two equations of motion say that ∂L/∂[overline]Ψ[\\overline]=-[overline]Ψ[\\overline]m and ∂L/∂Ψ=i[overline]Ψ[\\overline]γμ.
Oct 3, 2022.
What is the formula for the Dirac equation?
Dirac Equation Formula
��=��(x,t) is the electron wave function.
M is the electron mass at rest.
X, t is the spacetime coordinates. p₁, p₂, p₃ are the momentum components.
Why Lagrangian formalism?
One motivation for the development of the Lagrangian formalism on fields, and more generally, for classical field theory, is to provide a clean mathematical foundation for quantum field theory, which is infamously beset by formal difficulties that make it unacceptable as a mathematical theory.
The Lagrangian is L = T −V = m ˙y2/2−mgy, so eq. (6.22) gives ¨y = −g, which is simply the F = ma equation (divided through by m), as expected.
The solution is y(t) = −gt2/2+v0t+y0, as we well know.

What is Dirac Lagrangian?