Melosh transformation in interacting quark theories

Abstract

We make a general study of the existence of a Melosh-type transformation in interacting quark field theories quantized on the null plane. Following Carlitz and Tung this transformation is required to decompose the total angular momentum operators of these theories into mutually commuting orbital angular momentum and spin parts. This allows the identification of a U(6) \ifmmode\times\else\texttimes\fi{} U(6) \ifmmode\times\else\texttimes\fi{} O(3) classification group in these theories. It is shown that the requirement of commutativity between the generators of the U(6) \ifmmode\times\else\texttimes\fi{} U(6) subgroup and the three momentum operators ${P}^{+}$, ${\stackrel{\ensuremath{\rightarrow}}{P}}^{\ensuremath{\perp}}$ generating translations on the null plane, when combined with the spin properties of the former, automatically assures the exact conservation of the entire U(6) \ifmmode\times\else\texttimes\fi{} U(6) algebra in a Poincar\'e-invariant theory. A part of this transformation which is bilinear in the quark field is shown to exist in these theories. This part commutes with the operators ${P}^{+}$ and ${\stackrel{\ensuremath{\rightarrow}}{P}}^{\ensuremath{\perp}}$ showing that the breaking of U(6) \ifmmode\times\else\texttimes\fi{} U(6) symmetry can take place only through the quark pair terms appearing in the transformation.