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 :(
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 :(