theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...

, one often analyzes theories with

supersymmetry In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories e ...

in which D-terms play an important role. In four dimensions, the minimal N=1 supersymmetry may be written using a

superspace Superspace is the coordinate space of a theory exhibiting supersymmetry. In such a formulation, along with ordinary space dimensions ''x'', ''y'', ''z'', ..., there are also "anticommuting" dimensions whose coordinates are labeled in Grassmann numb ...

. This superspace involves four extra fermionic coordinates

\theta^1,\theta^2,\bar\theta^1,\bar\theta^2

, transforming as a two-component

spinor In geometry and physics, spinors are elements of a complex vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a slight ...

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. The generic kind of superfields, typically a

vector superfield In theoretical physics, there are many theories with supersymmetry (SUSY) which also have internal gauge symmetries. Supersymmetric gauge theory generalizes this notion. Gauge theory A gauge theory is a mathematical framework for analysing gau ...

, indeed depend on all these coordinates. The last term in the corresponding expansion, namely

D \theta^1\theta^2\bar\theta^1\bar\theta^2

, is called the D-term. Manifestly supersymmetric

Lagrangian Lagrangian may refer to: Mathematics * Lagrangian function, used to solve constrained minimization problems in optimization theory; see Lagrange multiplier ** Lagrangian relaxation, the method of approximating a difficult constrained problem with ...

s may also be written as

integral In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented i ...

s over the whole superspace. Some special terms, such as the

superpotential In theoretical physics, the superpotential is a function in supersymmetric quantum mechanics. Given a superpotential, two "partner potentials" are derived that can each serve as a potential in the Schrödinger equation. The partner potentials hav ...

, may be written as integrals over

\theta

s only, which are known as

F-term 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 coo ...

s, and should be contrasted with the present D-terms.

See also