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My opinions and recommendations:
a) When writing a paper, or writing in my notebooks, I use \nabla^2 in
all cases, in two, three, four, or however-many dimensions.
I see no reason to change symbology when switching from three dimensions
to four. IMHO if you do things right, the same concepts and the same
symbology should work just fine in all dimensions from two on up. This
is a sufficient reason for deprecating the \box form of the d'Alembertian.