Spin change of Fermions and quantum energy spectrum

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SUMMARY

The discussion centers on the behavior of spin-1/2 fermions in quantum mechanics, specifically addressing the creation and annihilation of these particles. It is established that fermions must appear or disappear in pairs to maintain the integrity of angular momentum, as changing the total angular momentum by a half-integer value is prohibited by the su(2)-Lie algebra. The spin flip of a single spin-1/2 fermion from +1/2 to -1/2 is permissible and does not violate these principles.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with spin-1/2 particles
  • Knowledge of angular momentum algebra
  • Basic concepts of Lie algebra, specifically su(2)
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  • Study the implications of the su(2)-Lie algebra in quantum mechanics
  • Explore the creation and annihilation operators for fermions
  • Learn about the role of spin in particle physics
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Physicists, quantum mechanics students, and researchers interested in particle physics and the behavior of fermions in quantum systems.

claymine
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Okay i was reading abrikosov's book and he said since in QM spin only changes by integer values boson excitiation happens one at a time and fermion ALWAYS appears or disappears in pairs. but isn't change from a spin up to spin down 1/2 to -1/2? or i had the wrong convention which |1/2| shouldve been the story?

Thank you
 
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I guess, what's meant is that in the creation of particles a spin-1/2 fermion can only be created in pairs, because otherwise you'd change the total angular momentum of the system by a half-integer value, which however is impossible due to the angular-momentum algebra (i.e., the su(2)-Lie algebra).

Of course there's nothing that prevents the spin flip from 1/2 to -1/2 of a single spin-1/2 fermion.
 
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