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.
References
- Fuchs, J (1994). "Fusion rules in conformal field theory". Fortschritte der Physik/Progress of Physics. 42 (1994): 1–48. arXiv:hep-th/9306162. Bibcode:1994ForPh..42....1F. doi:10.1002/prop.2190420102. S2CID 14139601.
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