Dirac–von Neumann axioms

In mathematical physics, the Dirac–von Neumann axioms give a mathematical formulation of quantum mechanics in terms of operators on a Hilbert space.

They were introduced by Paul Dirac in 1930 and John von Neumann in 1932.

is a fixed complex Hilbert space of countably infinite dimension.

If the C*-algebra is the algebra of all bounded operators on a Hilbert space

This is similar to Dirac's formulation of quantum mechanics, though Dirac also allowed unbounded operators, and did not distinguish clearly between self-adjoint and Hermitian operators.