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For conserved local currents ?µjµ(x)=0 in quantum field theory it is shown that anR-dependence of aR(x0) inj0(fR(x)·aR(x0)) leads to nicer properties than a fixed a(x0). The behaviour of<img src="/fulltext-image.asp?format=htmlnonpaginated&src=T2W212P0243N52K0_html\220_2005_Article_BF01609406_TeX2GIFIE1.gif" border="0" alt="$$\mathop {\lim }\limits_{R \to \infty } \left\| {j_0 (f_R (x) \cdot \alpha _R (x_0 )\Omega } \right\|$$" /> ?j0(fR(x)·aR(x0)O? is discussed under this aspect.

Symmetry conservation and integrals over local charge densities in quantum field theory