Wikipedia
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 $\theta^1,\theta^2,\bar\theta^1,\bar\theta^2$, transforming as a two-component spinor and its conjugate.
Every superfield—i.e. a field that depends on all coordinates of the superspace—may be expanded with respect to the new fermionic coordinates. There exists a special kind of superfields, the so-called chiral superfields, that only depend on the variables θ but not their conjugates. The last term in the corresponding expansion, namely Fθθ, is called the F-term. 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. This is significant because then ∫dx F(x) 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 θs only. They are also referred to as F-terms, much like the terms in the ordinary potential that arise from these terms of the supersymmetric Lagrangian.
In Japanese patent law, F-term is a system for classifying Japanese patent documents according to the technical features of the inventions described in them. It is not a replacement for the International Patent Classification (IPC) or other patent classifications, but complements other systems by providing a means for searching documents from different viewpoints. A symbol attached to a patent document, indicating that the invention disclosed in the document has a particular technical feature, is also called an F-term.