Wess-Zumino

In theoretical physics, the Wess–Zumino model has become the first known example of an interacting four-dimensional quantum field theory with linearly realised supersymmetry. In 1974, Julius Wess and Bruno Zumino studied, using modern terminology, dynamics of a single chiral superfield (composed of a complex scalar and a spinor fermion) whose cubic superpotential leads to a renormalizable theory.

The Lagrangian of the free massless Wess–Zumino model in four-dimensional spacetime with flat metric ${\displaystyle \mathrm {diag} (-1,1,1,1)}$ is

with ${\displaystyle S}$ a scalar field, ${\displaystyle P}$ a pseudoscalar field and ${\displaystyle \psi }$ a Majorana spinor field. The action is invariant under the transformations generated by the superalgebra. The infinitesimal form of these transformations is:

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