This Lagrangian is missing the interaction term. Gene --- Scott Fenton <sctfen@gmail.com> wrote:
Not quite sure if this is exactly what you're looking for, but the Lagrangian for Quantum Electrodynamics (in units where c=hbar=1) is:
L = psi* (i gamma^mu D_mu - m) psi - (1/4) F_(mu nu) F^(mu nu)
(from the Wikipedia article for QED). Variables are as follows: psi: wavefunction gamma: Dirac matricies D: covariant derivative m: mass of an electron
-Scott Fenton
On 7/18/06, Eugene Salamin <gene_salamin@yahoo.com> wrote:
Can one of the advanced theoretical physics people here answer this question. Is there a Lagrangian, either classical or quantum, that describes the dynamics of the electromagnetic field together with charged particles, electrons if we need to be specific? From what I see, there is a Lagrangian in which the field variables are varied, with fixed charges and currents, to give Maxwell's equations. A second Lagrangian with particle coordinates varied, for fixed fields, gives the Lorentz force law. And finally a third Lagrangian (see Landau & Lifschitz, "Classical Theory of Fields") tries to meld the two together, but is only valid to order (v/c)^2. I am looking for One Lagrangian that rules them all, one that determines the exact theory of electrodynamics.
Gene
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