 The third important problem for standard QFT which prompted reformulations is the existence of inequivalent representations. In the context of quantum mechanics, Schrödinger, Dirac, Jordan and von Neumann realized that Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics are just two (unitarily) equivalent representations of the same underlying abstract structure, i.e., an abstract Hilbert space \(\mathcal{H}\) and linear operators acting on this space. We are merely dealing with two different ways for representing the same physical reality, and it is possible to switch between these different representations by means of a unitary transformation, i.e. an operation that is analogous to an innocuous rotation of the frame of reference. Representations of some given algebra or group are sets of mathematical objects, like numbers, rotations or more abstract transformations (e.g. differential operators) together with a binary operation (e.g. addition or multiplication) that combines any two elements of the algebra or group, such that the structure of the algebra or group to be represented is preserved. This means that the combination of any two elements in the representation space, say \(a\) and \(b\), leads to a third element which corresponds to the element that results when you combine the elements corresponding to \(a\) and \(b\) in the algebra or group that is represented. In 1931 von Neumann gave a detailed proof (of a conjecture by Stone) that the canonical commutation relations (CCRs) for position coordinates and their conjugate momentum coordinates in configuration space fix the representation of these two sets of operators in Hilbert space up to unitary equivalence (von Neumann’s uniqueness theorem). This means that the specification of the purely algebraic CCRs suffices to describe a particular physical system.