sector to produce momentum transfer. These so-called partially twisted boundary conditions eliminate the need to regenerate gauge configurations for each value of the twisting parameters, and allow moments and radii of flavor changing operators to be extracted at zero lattice momentum (up to volume corrections [@Sachrajda:2004mi]). This procedure has been studied in numerical simulations: for extracting $f_\pi$ [@Flynn:2005in], and for determining $K \to \pi$ matrix elements [@Guadagnoli:2005be].

In this work, we point out that the vector flavor symmetry $SU(2)_V$ of QCD relates matrix elements of isospin changing operators to matrix elements of isovector operators. Thus the form factors of the latter can be accessed at continuous momentum transfer by calculating flavor changing matrix elements on the lattice. This result holds for quark bilinear operators of arbitrary spin and Lorentz structure. Our discussion is organized as follows. In Sect. \[s:SU(2)\_V\], we derive the relations between matrix elements related by an isospin rotation. Next in Sect. \[s:extension\], we detail how these relations can be utilized on the lattice with partially twisted boundary conditions. The dynamical effects of the boundary conditions are discussed in Sect. \[s:example\], where the volume effects for the nucleon isovector magnetic moment are presented. We end with a brief 