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Statistical isotropy and statistical reflection symmetry allow the spectral tensor to contain only ${\delta }_{ij}$ and $k_i{k}_j$:The solenoidal magnetic-field constraint is essential here. Taking its Fourier transform gives $k_i{\hat{B}}_i=0$, hence $k_i{\hat{C}}_{ij}=0$ and $A+D{k}^2=0$. Thus the spectral tensor is a scalar multiple of the transverse projector of a vector field. Its trace is $2A$, so the prescribed normalization givesThis is the solenoidal isotropic spectral tensor. Without the solenoidal condition, isotropy and reflection symmetry would leave two scalar functions. Without reflection symmetry, an antisymmetric term proportional to $i{ϵ}_{ijm}{k}_m$ could additionally encode magnetic helicity.

Statistical reflection symmetry means that the joint distributions of a random field are unchanged by a simultaneous spatial reflection, with each field component transformed according to its vector or pseudovector character. For an isotropic magnetic field, it excludes a parity-odd magnetic helicity contribution to the two-point spectral tensor.