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| {{Distinguish| Wess–Zumino–Witten model}}
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| In [[theoretical physics]], the '''Wess–Zumino model''' has become the first known example of an interacting four-dimensional [[quantum field theory]] with [[supersymmetry]], at least in the Western world. In 1974, [[Julius Wess]] and [[Bruno Zumino]] studied, using modern terminology, dynamics of a single [[chiral superfield]] (composed of a complex [[scalar (physics)|scalar]] and a [[spinor]] [[fermion]]) whose cubic [[superpotential]] leads to a [[renormalizable]] theory.
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| <!--==Introduction==-->
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| The Lagrangian of the ''free'' massless Wess–Zumino model in four-dimensional spacetime with flat metric <math>\mathrm{diag}(-1,1,1,1)</math> is
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| ::<math>
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| \mathcal{L}=-\frac{1}{2}(\partial S)^{2}-\frac{1}{2}(\partial P)^{2}-\frac{1}{2}\bar{\psi} \partial\!\!\!/ \psi
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| </math>
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| with <math>S</math> a scalar field, <math>P</math> a pseudoscalar field and <math>\psi</math> 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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| ::<math>\delta_{\epsilon} S=\bar{\epsilon} \psi</math>
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| ::<math>\delta_{\epsilon} P =\bar{\epsilon} \gamma_{5} \psi</math>
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| ::<math>\delta_{\epsilon} \psi =\partial\!\!\!/ (S+P\gamma_{5})\epsilon </math>
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| where <math>\epsilon</math> is a Majorana spinor-valued transformation parameter and <math>\gamma_{5}</math> is the [[Chirality (physics)#Chiral theories|chirality operator]].
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| Invariance under a (modified) set of supersymmetry transformations remains if one adds mass terms for the fields, provided the masses are equal. It is also possible to add interaction terms under some algebraic conditions on the coupling constants, resulting from the fact that the interactions come from [[superpotential]] for the [[chiral superfield]] containing the fields <math>S</math>, <math>P</math> and <math>\psi</math>.
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| ==References==
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| *{{cite arxiv |first=J. M. |last=Figueroa-O'Farrill |title=Busstepp Lectures on Supersymmetry |year=2001 |eprint=hep-th/0109172 }}
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| *{{cite journal |first=J. |last=Wess |first2=B. |last2=Zumino |title=Supergauge transformations in four dimensions |journal=Nuclear Physics B |volume=70 |issue=1 |pages=39–50 |year=1974 |doi=10.1016/0550-3213(74)90355-1 |bibcode=1974NuPhB..70...39W }}
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| {{Quantum field theories}}
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| {{DEFAULTSORT:Wess-Zumino model}}
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| [[Category:Supersymmetry]]
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| {{quantum-stub}}
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