Abstract
Localization of relativistic particles and their position-momentum uncertainty relations are not yet fully understood. We discuss two schemes of photon localization that are based on the energy density. One scheme produces a positive operator-valued measure for localization. It coincides with the number density operator and reproduces an effective $3\ifmmode\times\else\texttimes\fi{}3$ polarization density matrix. Another scheme results in a probability distribution that is conditioned on the detection. In both schemes the uncertainty relations for transversal position and momentum approach the Heisenberg bound $\ensuremath{\Delta}p\ensuremath{\Delta}z=\frac{1}{2}\ensuremath{\hbar}$.
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