  We present a frame- and reparametrisation-invariant formalism for quantum
field theories that include fermionic degrees of freedom. We achieve this using
methods of field-space covariance and the Vilkovisky-DeWitt (VDW) effective
action. We explicitly construct a field-space supermanifold on which the
quantum fields act as coordinates. We show how to define field-space tensors on
this supermanifold from the classical action that are covariant under field
reparametrisations. We then employ these tensors to equip the field-space
supermanifold with a metric, thus solving a long-standing problem concerning
the proper definition of a metric for fermionic theories. With the metric thus
defined, we use well-established field-space techniques to extend the VDW
effective action and express any fermionic theory in a frame- and
field-reparametrisation-invariant manner.
