Werner Heisenberg the lattice theory of crystals in 1921. While matrices were used in these cases, the algebra of matrices with their multiplication did not enter the picture as they did in the matrix formulation of quantum mechanics. In 1928, Albert Einstein nominated Heisenberg, Born, and Jordan for the Nobel Prize in Physics, The announcement of the Nobel Prize in Physics for 1932 was delayed until November 1933. It was at that time that it was announced Heisenberg had won the Prize for 1932 "for the creation of quantum mechanics, the application of which has, , led to the discovery of the
Heisenberg group an overall phase factor. The phase factor is needed to obtain a group of operators, since translations in position space and translations in momentum space do not commute. The key result is the Stone–von Neumann theorem, which states that every (strongly continuous) irreducible unitary representation of the Heisenberg group in which the center acts nontrivially is equivalent to formula_48 for some formula_27. Alternatively, that they are all equivalent to the Weyl algebra (or CCR algebra) on a symplectic space of dimension 2"n". Since the Heisenberg group is a one-dimensional central extension of formula_57, its irreducible unitary representations can be viewed