Negative energy in Dirac equation

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SUMMARY

The discussion centers on the implications of the Dirac equation, particularly regarding negative energy states for electrons. Dirac proposed that all negative energy states are filled, preventing electrons from transitioning to these states and emitting photons. While some participants view the Dirac sea model as contrived, it remains a successful phenomenological model that led to the discovery of anti-particles. The conversation also touches on the transition from the Dirac equation to Quantum Field Theory (QFT), where wavefunctions are reinterpreted as fields, resolving many of the original issues.

PREREQUISITES
  • Understanding of the Dirac equation and its implications in quantum mechanics.
  • Familiarity with concepts of negative energy states and the Dirac sea model.
  • Knowledge of Quantum Field Theory (QFT) and its interpretation of wavefunctions.
  • Basic grasp of particle physics, including the concept of anti-particles.
NEXT STEPS
  • Research the Dirac equation and its solutions in detail.
  • Explore the concept of the Dirac sea and its criticisms.
  • Study Quantum Field Theory and its approach to wavefunctions as fields.
  • Investigate the relationship between negative energy states and anti-particles in particle physics.
USEFUL FOR

Physicists, students of quantum mechanics, and anyone interested in the foundational concepts of particle physics and the implications of the Dirac equation.

kahoomann
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When Dirac solved his equation for electron, he found out there are negative energy states.
My question is why electrons won't jump from positive energy state to negative energy states and release energy as photon?

Dirac proposed that all negative energy states have been filled so electrons can't jump to negative energy states. It's clearly contrived
 
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kahoomann said:
When Dirac solved his equation for electron, he found out there are negative energy states.
My question is why electrons won't jump from positive energy state to negative energy states and release energy as photon?

Dirac proposed that all negative energy states have been filled so electrons can't jump to negative energy states. It's clearly contrived
Yep. You can say that the Dirac sea picture is kinda artificial, but, anyway, it's a successful phenomenological model.
Actually, Dirac only solved the negative probability problem manifestly. However, the Dirac equation still has negative energy solution. This motivates the discovery of anti-particles.

Yet the complete exact solution is given by QFT where the field solutions for the equation of motion are no longer interpreted as the wavefunctions. That is, [tex]\psi^*\psi[/tex] is not probability anymore. The wavefunctions become fields which are recognized as operators. And the problems disappear naturally.

BTW, I remember that I see somewhere an article saying that the Dirac sea picture is somehow can be thought of as an aether. (I'm not very clear about this.)
 

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