# Fusion rules

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{{Short description|Tensor product decomposition rules in representation theory}}
In [mathematics](/source/mathematics) and [theoretical physics](/source/theoretical_physics), '''fusion rules''' are rules that determine the exact decomposition of the [tensor product](/source/tensor_product) of two [representations](/source/group_representation) of a [group](/source/group_(mathematics)) into a [direct sum](/source/direct_sum_of_representations) of [irreducible representation](/source/irreducible_representation)s. The term is often used in the context of [two-dimensional conformal field theory](/source/two-dimensional_conformal_field_theory) where the relevant group is generated by the [Virasoro algebra](/source/Virasoro_algebra), the relevant representations are the [conformal families](/source/conformal_family) associated with a [primary field](/source/primary_field) and the tensor product is realized by [operator product expansion](/source/operator_product_expansion)s. The fusion rules contain the information about the kind of families that appear on the right-hand side of these OPEs, including the multiplicities.

More generally, [integrable model](/source/integrable_model)s in 2 dimensions which aren't conformal field theories are also described by fusion rules for their charges.<ref>{{cite journal |arxiv = hep-th/9306162|last1 = Fuchs|first1 = J|title = Fusion rules in conformal field theory|journal = Fortschritte der Physik/Progress of Physics|volume = 42|issue = 1994|pages = 1–48|year = 1994|doi = 10.1002/prop.2190420102|bibcode = 1994ForPh..42....1F| s2cid=14139601 }}</ref>

== References ==
{{Reflist}}

Category:Conformal field theory

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