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 given action of the central Lie algebra element "z", up to a unitary equivalence: the nontrivial elements of the algebra are all equivalent to the usual position and momentum operators. Thus, the Schrödinger picture and Heisenberg picture are equivalent – they are just different ways of realizing this essentially unique representation. The same uniqueness result was used by David Mumford for discrete Heisenberg groups, in his theory of equations defining abelian varieties. This is a large generalization of the approach used in Jacobi's elliptic functions, which is the case of the modulo 2 Heisenberg group, of order 8. The simplest