In theoretical physics, one often analyzes theories with supersymmetry in which F-terms play an important role.
In four dimensions, the minimal N=1 supersymmetry may be written using a superspace.
This superspace involves four extra fermionic coordinates
, transforming as a two-component spinor and its conjugate.
Applying an infinitesimal supersymmetry transformation to a chiral superfield results in yet another chiral superfield whose F-term, in particular, changes by a total derivative.
is invariant under SUSY transformations as long as boundary terms vanish.
Thus F-terms may be used in constructing supersymmetric actions.
Manifestly-supersymmetric Lagrangians may also be written as integrals over the whole superspace.
Some special terms, such as the superpotential, may be written as integrals over