We analyze the global symmetries of ${ \cal N}=4$ supersymmetric mechanics involving $4n$-dimensional Quaternion-K\"ahler (QK) $1D$ sigma models on projective spaces $\mathbb{ H}{ \rm H}^n$ and $\mathbb{ H}{ \rm P}^n$ as the bosonic core. All Noether charges associated with global worldline symmetries are shown to vanish as a result of equations of motion, which implies that we deal with a severely constrained hamiltonian system. The complete hamiltonian analysis of the bosonic sector is performed.
Categories: hep-th