Editing Pauli exclusion principle (section)

=== Advanced quantum theory ===
According to the [[spin–statistics theorem]], particles with integer spin occupy symmetric quantum states, and particles with half-integer spin occupy antisymmetric states; furthermore, only integer or half-integer values of spin are allowed by the principles of quantum mechanics.
In relativistic [[quantum field theory]], the Pauli principle follows from applying a [[Rotation operator (quantum mechanics)|rotation operator]] in [[imaginary time]] to particles of half-integer spin.

In one dimension, bosons, as well as fermions, can obey the exclusion principle. A one-dimensional Bose gas with delta-function repulsive interactions of infinite strength is equivalent to a gas of free fermions. The reason for this is that, in one dimension, the exchange of particles requires that they pass through each other; for infinitely strong repulsion this cannot happen. This model is described by a quantum [[nonlinear Schrödinger equation]]. In momentum space, the exclusion principle is valid also for finite repulsion in a Bose gas with delta-function interactions,<ref>{{Cite journal|url=http://insti.physics.sunysb.edu/~korepin/pauli.pdf|title=Pauli principle for one-dimensional bosons and the algebraic Bethe ansatz|author1=A. G. Izergin|author2=V. E. Korepin|journal=Letters in Mathematical Physics|volume=6|issue=4|pages=283–288|date=July 1982|doi=10.1007/BF00400323|bibcode=1982LMaPh...6..283I|s2cid=121829553|access-date=2009-12-02|archive-date=2018-11-25|archive-url=https://web.archive.org/web/20181125205409/http://insti.physics.sunysb.edu/~korepin/pauli.pdf|url-status=dead}}</ref> as well as for [[Heisenberg model (quantum)|interacting spins]] and [[Hubbard model]] in one dimension, and for other models solvable by [[Bethe ansatz]]. The [[Stationary state|ground state]] in models solvable by Bethe ansatz is a [[Fermi energy|Fermi sphere]].