Francisco Neto, Antônio2017-09-142017-09-142013FRANCISCO NETO, A. Matula numbers, Gödel numbering and Fock space. Journal of Mathematical Chemistry, v. 51, p. 1802-1814, 2013. Disponível em: <https://link.springer.com/article/10.1007/s10910-013-0178-z>. Acesso em: 20 jul. 2017.1572-8897http://www.repositorio.ufop.br/handle/123456789/8732By making use of Matula numbers, which give a 1-1 correspondence between rooted trees and natural numbers, and a Gödel type relabelling of quantum states, we construct a bijection between rooted trees and vectors in the Fock space. As a by product of the aforementioned correspondence (rooted trees ↔ Fock space) we show that the fundamental theorem of arithmetic is related to the grafting operator, a basic construction in many Hopf algebras. Also, we introduce the Heisenberg–Weyl algebra built in the vector space of rooted trees rather than the usual Fock space. This work is a cross-fertilization of concepts from combinatorics (Matula numbers), number theory (Gödel numbering) and quantum mechanics (Fock space).en-USrestritoRooted treesHopf algebraGödel relabellingHeisenberg–Weyl algebraArtigo publicado em periodicohttps://link.springer.com/article/10.1007/s10910-013-0178-zhttps://doi.org/10.1007/s10910-013-0178-z