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:
“Southerners, whose ancestors a hundred years ago knew the horrors of a homeland devastated by war, are particularly determined that war shall never come to us again. All Americans understand the basic lessons of history: that we need to be resolute and able to protect ourselves, to prevent threats and domination by others.”
—Jimmy Carter (James Earl Carter, Jr.)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)