Basic Properties
Free (non-interacting) fermionic fields obey canonical anticommutation relations, i.e., involve the anticommutators {a,b} = ab + ba rather than the commutators = ab − ba of bosonic or standard quantum mechanics. Those relations also hold for interacting fermionic fields in the interaction picture, where the fields evolve in time as if free and the effects of the interaction are encoded in the evolution of the states.
It is these anticommutation relations that imply Fermi–Dirac statistics for the field quanta. They also result in the Pauli exclusion principle: two fermionic particles cannot occupy the same state at the same time.
Read more about this topic: Fermionic Field
Famous quotes containing the words basic and/or properties:
“We can’t nourish our children if we don’t nourish ourselves.... Parents who manage to stay married, sane, and connected to each other share one basic characteristic: The ability to protect even small amounts of time together no matter what else is going on in their lives.”
—Ron Taffel (20th century)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)