Feynman Diagrams For Pedestrians - Herbstschule Maria Laach

∴ the formalism is consistent, if all quantum numbers are reversed on the negativemass shell∵ in a stationary, i. e. time independent, state, the casescan not be distinguished.Q, ⃗p−Q, −⃗p∴ the states on the negative mass shell describe not particles with “negative energy”,but anti particles with opposite quantum numbers instead!• in stationary states, this can be taken a step further: instead of anti particlesmoving forward in time . . .• . . . one can use particles moving backward in time, without noticing a differencein the overall balance!• caveat: it is not (yet) obvious that this makes sense of interactions are switchedon . . .• . . . will be shown later.• NB: this is a calculationally convenient interpretation — there is no time travelgoing on, since we’re in a steady state• The equivalent picture with anti particles moving forward in time requires thefull machinery of quantum field theory2.4 Dirac Equation• task: find “objects” γ µ , such that(γ µ ∂ µ ) 2 = ∂ 2 (31)• because the solutions of the Dirac equation(iγ µ ∂ µ − m) ψ(x) = 0 (32)automagically satisfy the die Klein-Gordon equation as well(iγ µ ∂ µ + m) (iγ µ ∂ µ − m) ψ(x) = ( −∂ 2 − m 2) ψ(x) = 0 (33)7