In mathematics and theoretical physics, fusion rules are rules that determine the exact decomposition of the tensor product of two representations of a group into a direct sum of irreducible representations.
The term is often used in the context of two-dimensional conformal field theory where the relevant group is generated by the Virasoro algebra, the relevant representations are the conformal families associated with a primary field and the tensor product is realized by operator product expansions.
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 models in 2 dimensions which aren't conformal field theories are also described by fusion rules for their charges.
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