- #1
itssilva
- 55
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From introductory courses on EM, I was given 'sketchy' proofs that, in a EM field in vacuum, magnetic energy density is B² and electric energy density is E² (bar annoying multiplication factors; they just get under my skin, I'll skip them all in the following). Other facts of life: -FμνFμν, the free EM Lagrangian (density), goes about like B² - E², which is an invariant, and δ(jμAμ - FμνFμν) = 0, or something, = Maxwell's equations (ME). Nice; however, Lagrangians are supposed to be energy - for a nonrelativistic test particle, L is just T - V -, and this is mysterious: why did someone put tensor F in the definition of the free EM Lagrangian, if it doesn't give the total energy density of the EM field in vacuum B²+ E² ? (If one can't find some other tensor F' and correct the full Lagrangian to give the ME, that can't be done, but in that case I want to know what F means, since ju is supposed to be a Dirac invariant that couples to the field, which vanishes if the matter field does not interact with the EM field; if that sign in the E² were right, I'd be unashamed to call F's contraction the kinetic energy of the free field).