Newton Wigner Position

This requirement rules out the standard position operator (multiplication by x), because it does not commute with the sign of the energy. The most prominent operator that leaves the positive energy subspace invariant is the Newton-Wigner position operator. Together with any other position operator that has the same property, it leads to inconsistencies with relativistic causality (see [9],... 

The point is that the photon creation and annihilation operators are defined in QED as nonlocal objects. In other words, the photon number operator gives the total number of photons in the volume of quantization without specification of their spacetime location [14,15]. Moreover, it has been proved by Newton and Wigner [16] that no position operator can exist for the photon. There is a widespread belief that the maximum precise localization appears in the form of... 

X is therefore a perfectly sensible position operator in the Dirac representation its properties were studied in detail by Newton and Wigner [60]. For more information see, for example, [61, 1.6]. 

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