Explain the Physical implications behind the exchange antisymmetry condition of fermions. This condition forms the basis of the pauli principle but I can't find/understand what happens physically that requires then the presence of a minus sign upon particle interchange.
Answer
To perform canonical quantization of a fermion field, we write the field in creation and annihilation operators. Writing the Hamiltonian in those creation and annihilation operators, we find that the energy of a field is unbounded from below (it can be as negative as you like).
This would be a disaster; a field could forever decay to lower energy states by e.g. the emission of a photon. That is not what we see.
If, however, we insist that the field obeys an anti-commutation rule (the Pauli exclusion principle), the energy is bounded from below (cannot be as small as you like). The situation is saved.
To summarise: physically, fermions must obey the Pauli exclusion principle, because if they did not, they could forever decay to lower energy states. For detail and the mathematics, see any introductory book on quantum field theory.
No comments:
Post a Comment