F-term
Encyclopedia
In theoretical physics
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...

, one often analyzes theories with supersymmetry
Supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...

 in which F-terms play an important role. In four dimensions, the minimal N=1 supersymmetry may be written using a superspace
Superspace
"Superspace" has had two meanings in physics. The word was first used by John Wheeler to describe the configuration space of general relativity; for example, this usage may be seen in his famous 1973 textbook Gravitation....

. This superspace involves four extra fermionic coordinates , transforming as a two-component spinor
Spinor
In mathematics and physics, in particular in the theory of the orthogonal groups , spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the space of spinors cannot be built up in a unique and natural way from spatial vectors...

 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 superfield
Chiral superfield
In theoretical physics, one often analyzes theories with supersymmetry in which chiral superfields play an important role. In four dimensions, the minimal N=1 supersymmetry may be written using the notion of superspace...

s, that only depend on the variables but not their conjugates. The last term in the corresponding expansion, namely , 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 is invariant under SUSY transformations as long as boundary terms vanish. Thus F-terms may be used in constructing supersymmetric actions.

Manifestly-supersymmetric Lagrangian
Lagrangian
The Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...

s may also be written as integral
Integral
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...

s over the whole superspace. Some special terms, such as the superpotential
Superpotential
Superpotential is a concept from particle physics' supersymmetry.-Example of superpotentiality:Let's look at the example of a one dimensional nonrelativistic particle with a 2D internal degree of freedom called "spin"...

, may be written as integrals over s 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.
The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
x
OK