In physics, the canonical commutation relation is the relation

among the position x and momentum p of a point particle in one dimension, where [x,p] = xp - px is the so-called commutator of x and p, i is the imaginary unit and is the reduced Planck's constant. This relation is attributed to Heisenberg, and it implies his uncertainty principle.

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	Canonical commutation relation - Wikipedia, the free encyclopedia (563 words) In physics, the canonical commutation relation is the relation This relation is attributed to Heisenberg, and it implies his uncertainty principle. The uniqueness of the canonical commutation relations between position and momentum is guaranteed by the Stone-von Neumann theorem. Bosonic field at AllExperts (476 words) Those relations also hold for interacting bosonic 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. In fact, the commutation or anti-commutation relations are assumed based on whether the theory one intends to study corresponds to particles obeying Bose-Einstein or Fermi-Dirac statistics. In this context the spin remains an internal quantum number that is only phenomenologically related to the statistical properties of the quanta.It must be stressed that such non-relativistic fields arise merely as an extremely convenient 're-packaging' of the many-body wave function describing the state of the system.
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