Dirac's explanation of negative energy states

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SUMMARY

Dirac's explanation of negative energy states in his equation is fundamentally tied to the concept of fermions, where all negative energy states are occupied, leading to the observation of "holes" in the negative energy sea. This explanation, however, fails when applied to bosons as described by the Klein-Gordon equation, indicating that Dirac's argument lacks consistency outside of quantum field theory (QFT). The discussion concludes that a comprehensive understanding of negative energy solutions requires the formalism of QFT, rendering Dirac's "hole in a sea" argument historically significant but insufficient for modern physics.

PREREQUISITES
  • Understanding of Dirac's equation and its implications for electron wave functions
  • Familiarity with the concepts of fermions and bosons in quantum mechanics
  • Knowledge of the Klein-Gordon equation and its application to scalar particles
  • Basic principles of quantum field theory (QFT)
NEXT STEPS
  • Study the formalism of quantum field theory (QFT) to grasp the creation and annihilation operators
  • Explore the differences between fermions and bosons in quantum mechanics
  • Read "Quantum Mechanics" by Schiff for a detailed explanation of negative energy solutions
  • Investigate the implications of the Klein-Gordon equation in particle physics
USEFUL FOR

Physicists, students of quantum mechanics, and researchers interested in the foundations of quantum field theory and the behavior of particles in relativistic contexts.

paweld
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I wonder whether Dirac explanation of paradox of negative energy solutions
of his equation is viable. Of course this paradox is absent in QFT but if
we treat Dirac equation as an equation for wave function of electron
the negative energy solution are a puzzle. Acording to Dirac we don't
observe negative energy particles because all states with negative energy are
occupied. What we observe is a "hole in negative energy see". However
for stability of vacuum we have to additionally assume that the described particles
are fermions (states with some electrons are stable as all states with lower energy
are occupied and two electrons cannot occupy the same state). If we consider
the Klein-Gordon equation describing scalar particles (bosons) the Dirac's explanation
doesn't work. So in my opinion it's impossible to consistently explain the negative
energy solutions of relativistic wave equations not using formalism of QFT
(the filed then becomes an operator which destroys and creates particles).
So Dirac "hole in a see" argument has only historical meaning.
Am I right?
 
Physics news on Phys.org
yes you are right. but for more explanation you can refer to quantum mechanics by schiff
,there he has elaborately given.
 

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