- #1
pellman
- 684
- 5
In general what does a Lagrangian for a system consisting of interacting fields and particles look like?
It can't be, for example,
[tex]L=\sum{\frac{1}{2}mv_j^2+A(x_j)\inner v_j}[/tex]
That would be for a system of particles in a fixed, i.e. "background", field. I'm interested in how we can mix particles and fields in Lagrangian mechanics. I know how to write down, as above, the Lagrangian for particles influenced by a field. And I know how to write down a Lagrangian (density) for a field with fixed (continuum) sources. But what does a Lagrangian (density?) that governs both fields and discrete sources look like?
No need to lay out the most general case. Just a simple example will suffice.
It can't be, for example,
[tex]L=\sum{\frac{1}{2}mv_j^2+A(x_j)\inner v_j}[/tex]
That would be for a system of particles in a fixed, i.e. "background", field. I'm interested in how we can mix particles and fields in Lagrangian mechanics. I know how to write down, as above, the Lagrangian for particles influenced by a field. And I know how to write down a Lagrangian (density) for a field with fixed (continuum) sources. But what does a Lagrangian (density?) that governs both fields and discrete sources look like?
No need to lay out the most general case. Just a simple example will suffice.