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Quantum Physics
Dirac's solution to the Klein-Gordon equation
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[QUOTE="vanhees71, post: 6060728, member: 260864"] The original argument by Dirac was flawed. His heuristics, however, lead to an utmost important step in the way to our recent understanding, namely the Dirac equation for spin-1/2 particles. What Dirac first missed was the fact that there's no consistent one-particle theory for interacting relativistic particles (or even for the simpler case of relativistic particles in an external field). Nowadays the reason for this is obvious, because we have a lot of experience with relativistic particles by the use of high-energy particle accelerators: At relativistic energies interactions among particles or of particles moving in an external field there's always some probability that new particles get created or the original particles get destroyed and other particles or radiation is produced. That's why a single-particle interpretation of the Dirac equation (and any other relativistic wave equation) fails. Dirac's true genius concerning his discovery of his wave equation thus is that he realized precisely this: You need a many-particle picture to interpret the equation right. Then he had another ingenious idea, namely the "Dirac sea". The idea was to get rid of the "negative-energy states" by assuming that these states are all occupied with electrons. In interactions at high enough energies you can kick out electrons of this sea, and since we interpret the completely filled sea (and no electrons present) as "the vacuum", the holes in the sea appear as positively charged particles with all other properties (mass and spin) the same as for electrons. That was the prediction of the existence of anti-electrons or positrons. Dirac could even work out quantum electro dynamics in terms of this hole theory. This formulation of QED is, however pretty complicated, and it's clear that the "Dirac sea" is another heuristics, because we don't see an infinite negative charge anywhere. That's why nowadays we don't teach the old-fashioned hole theory anymore but formulate relativistic QT right away as relativistic QFT, which is the natural formulation for the situation that particles get created and destroyed in interactions. [/QUOTE]
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Dirac's solution to the Klein-Gordon equation
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