Question

If we have Lagrangian $\mathcal{L} = \frac{i}{2} \left[ \bar{\psi} \gamma^\mu \partial_\mu \psi - (\partial_\mu \bar{\psi}) \gamma^\mu \psi \right] - m \bar{\psi} \psi$ find the equation of motion of this system where the field are $\psi$ and $\bar{\psi}$ $\gamma^\mu$: Constant matrix.

          If we have Lagrangian
$\mathcal{L} = \frac{i}{2} \left[ \bar{\psi} \gamma^\mu \partial_\mu \psi - (\partial_\mu \bar{\psi}) \gamma^\mu \psi \right] - m \bar{\psi} \psi$
find the equation of motion of this system
where the field are $\psi$ and $\bar{\psi}$
$\gamma^\mu$: Constant matrix.

If we have Lagrangian
ℒ = (i)/(2)[ ψ̅γ^μ∂μψ - (∂μψ̅) γ^μψ] - m ψ̅ψ
find the equation of motion of this system
where the field are ψ and ψ̅
γ^μ: Constant matrix.

Added by -Ngeles S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Geeta Yadav

Step 1

So, we need to find the partial derivatives with respect to x and dx/dt. ∂L/∂(dx/dt) = iq ∂L/∂x = iq - 16x^3 Now, let's substitute these derivatives into the Lagrangian equation of motion: d/dt (∂L/∂(dx/dt)) - ∂L/∂x = 0 d/dt (iq) - (iq - 16x^3) = 0 i(dq/dt) - Show more…

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