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lavster
Apr17-11, 08:50 AM
1. The problem statement, all variables and given/known data

In my notes i have the following two equations written with no explanation where thehy came from... can someone help please!?

L=(u, x )= -mc\sqrt(u^{\beta} u_\beta)-\frac{q}{c}A^{\alpha}u_\alpha,

L(v,r, t) = -mc^2(1-\frac{v^2}{c^2})-\phi +\frac{q}{c}vA

L is lagrangian, m mass c speed of light u is speed, A is potential four vector made up of scalar (phi) and vector potential A

2. Relevant equations

L = \frac{1}{2}m u_{\alpha} u^{\alpha}-\frac{1}{c}A^{\alpha}j_{\alpha}-\frac{1}{16\pi}F^{\alpha\beta}F_{\alpha\beta}

F is electromagnetic field tensor



3. The attempt at a solution

I have no idea :(

hunt_mat
Apr18-11, 03:20 PM
Have you tried putting them through the Euler-Lagrange equations and seeing what you
get? It's the case that you usually have to guess at lagrangian, so there is no explanation from where they came from.