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wdlang
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Dirac's equation is just a low energy limit of QED
it is not exact
it is not exact
It predicts a g-factor of 2, which is not correct (but a good approximation) - not surprising, as Dirac's equation is not QED.andrien said:it is exact.
mfb said:It predicts a g-factor of 2, which is not correct (but a good approximation) - not surprising, as Dirac's equation is not QED.
mfb said:It predicts a g-factor of 2, which is not correct (but a good approximation) - not surprising, as Dirac's equation is not QED.
No, it isn't. You can't derive g=2 w/o using SR.DrDu said:Actually, the value 2 for the g factor is the non-relativistic result. So you don't need the Dirac equation at all to derive it.
tom.stoer said:No, it isn't. You can't derive g=2 w/o using SR.
Interesting!dextercioby said:Sure you can. Check out the work by Levy-Leblond in the '60s. And particularly his article with the reference:
Comm. math. Phys. 6, 286--311 (1967) .
vanhees71 said:The only trouble is that this is not a unique prescription.
The difference is that the Dirac equation for a spin-1/2 particle naturally emerges from the analysis of the proper-orthochronous Poincare group augmented with parity invariance. The most natural Lagrangian for a spin-1/2 particle turns out to be the Dirac Lagrangian, leading to the first-order equation (in space and time). Then minimal coupling of an Abelian gauge field leads to QED with a (tree-level) value [itex]g=2[/itex].DrDu said:Yes, but this holds also true in case of the Dirac equation. Gauging the Klein Gordon equation evidently also does not yield a g factor as there is no spin.
Dirac's equation is a relativistic quantum mechanical wave equation that describes the behavior of fermions, such as electrons. It is important because it helped unify quantum mechanics with special relativity and led to the prediction of the existence of antimatter.
Dirac's equation is a foundational equation in quantum electrodynamics (QED), which is the quantum field theory that describes the interactions between electrically charged particles and electromagnetic fields. Dirac's equation allows for the description of the quantum behavior of electrons in QED.
Yes, Dirac's equation is still relevant in modern physics. It has been incorporated into the Standard Model of particle physics and is used to accurately describe the behavior of electrons and other fermions in various physical phenomena, such as particle collisions and the behavior of atoms.
Yes, Dirac's equation can be applied to other fermions such as protons, neutrons, and quarks. It is also used to describe the behavior of other fundamental particles in the Standard Model, such as muons and tau particles.
Dirac's equation has been incredibly successful in describing the behavior of fermions in various physical phenomena. However, it does not account for the effects of gravity and therefore cannot be used to describe the behavior of particles in gravitational fields. This limitation has led to the development of other equations, such as the Dirac-Kähler equation, which attempts to incorporate both quantum mechanics and general relativity.