Scaling theory of conserved current and universal amplitudes at anisotropic critical points

A scaling theory of conserved currents is studied at critical points with critical charge fluctuations. It is shown that the conserved current has no anomalous dimension even for anisotropic critical points. Many universal amplitudes are identified. One of the universal amplitudes at the critical points is ${\lim }_{(\mathit{k},\mathrm{\omega })\to 0\mathrm{\omega }}^{2\mathrm{-}\mathit{d}}$ ${\mathit{k}}^{\left(\mathit{z}\mathrm{-}\mathit{d}\right)}$ ${}_{}{}^{\left(2\mathrm{}\mathrm{-}\mathit{d}\right)}{}_{}{}^{}\mathrm{\sigma }$(ω)${]}^{\mathit{z}}$[κ(k)${]}^{2\mathrm{-}\mathit{d}}$, which reduces to the universal conductance in 2+1 dimensions. We find that the ratio √κχ /σ always approaches a constant as we approach the critical point. We also determine exponents of many scaling relations, using the scaling properties of the current.