By Paul Arthur Schilpp
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Additional info for Albert Einstein: Philosopher-scientist, Edition: 1ST
3 Determination of the Energy-Momentum Tensor for a General Lagrange Density e(1/Ju, f}1/Ju/f)xJJ) where we have used In order to calculate the energy-momentum tensor we start with the Noether theorem: Each continuous symmetry transformation which leaves the Lagrange density invariant, corresponds to a conservation law and, hence, to a constant of motion. Specifically we shall discuss the conservation laws, which follow from the translational invariance of classical field theory. c does not explicitly depend on the coordinates.
8Ao) - lOf:. 122) yields or of:. 1 8cp 1 ( e)2 ine 8Ao [ cp 8t = 2mo +inV + ~A + eAo + 2moc2 & l/~- = [ -p2 2mO 1 e ine ine 8Ao - - A . p + eAo+-(VoA)+-2? 140) 41 This is the SchrOdinger equation for electromagnetic potentials. But be careful: In studying radiation problems we generally choose the Coulomb gauge, defined by div A =0 . In this case the term proportional to oAo/Ot must be included. Only in the Lorentz gauge, for which .!. 140) vanish. EXERCISE . . . . . . . . . . . . .
If one of the charge-like quantum numbers is not equal to zero, then 1Je has no physical meaning. l) (which are assumed to be different), then we can choose 1Je = 1. But if particles and antiparticles are identical, then (4) turns to be an eigenvalue equation 1M, p, J, A; 0, 0, 0, O)e = 1JeIM, p, J, A; 0, 0, 0, 0) (7) The eigenvalue 1Je is named C-parity. It is natural to postulate that the double application of the charge conjugation leads back to the original state. g. a two-particle state like (10) where each particle state I