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We revisit old ideas that smearing or blocking an SU(N) lattice gauge field,or averaging over an ensemble of fields created in the neighbourhood of thatfield, can reduce the high frequency fluctuations sufficiently that the naivelattice operator for the topological charge density is able to provide areliable measure of the topological charge of the field. We show that thesethree methods do indeed provide additional simple methods for calculating thetotal topological charge, with smearing particularly economical at currentcouplings. More interestingly, the ensemble average method can also be used toexpose the distribution in space-time of the topological charge and thisconceptually transparent, albeit computationally expensive, method provides auseful benchmark against which to compare other methods. Using this benchmarkwe find that a few smearing steps are also reliable in exposing thedistribution in space-time of the topological charge, thus providing a veryeconomical and simple method for doing so. We also use the same benchmark todetermine what is the number of `cooling' sweeps one needs to perform in orderto expose the charge density reliably.

More methods for calculating the topological charge (density) of SU(N) lattice gauge fields in 3+1 dimensions