Recently, unexpected relations between unrelated physical quantities such as Hall viscosity, conductivity and angular momentum have been proposed for certain condensed matter systems with broken parity. We derive the quantum field theory Ward identities originated from area preserving as well as conformal transformations for relativistic as well as non-relativistic systems. The relations among these physical quantities depend on the symmetries of the system. A special cases yields the well known relation: Hall viscosity is half the angular momentum.