Curiously, the fusion operation that is formalized by the notion of fusion bundles is mathematically reminiscent of (and physically of essentially the same intuitive nature as) the “star product” on closed string fields considered in string field theory [Witten (1986),Fig. 20]:

References

Konrad Waldorf, Transgression to Loop Spaces and its Inverse, I: Diffeological Bundles and Fusion Maps, Cah. Topol. Geom. Differ. Categ., 2012, Vol. LIII, 162-210 [arXiv:0911.3212, cahierstgdc:LIII]