Gauge Transformations and the Nematic to Smectic- A Transition

A continuum of θ-parametrized gauge transformations is used to relate the order-parameter correlation function, G_θ(→x, 0), in gauge θ to that in the transverse gauge (θ=π2). The exponent η_θ depends continuously on θ at an isotropic critical point. In the physical gauge (θ=0) in three dimensions ($d=3$), Caill\'e's results for reduced temperature $t<0$, and a finite susceptibility at $t=0$ at an isotropic critical point are found. For $t=0$ and $d=3$, the correlation lengths obtained from G₀ differ from those obtained from G_π2 and satisfy ${{{ξ}}_{{∥}}}ˣ{~}{{({{{ξ}}_{{⊥}}}ˣ)}²}{ln{{{ξ}}_{{⊥}}}ˣ}$.