Matula numbers, Gödel numbering and Fock space.
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2013
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Resumo
By 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).
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Rooted trees, Hopf algebra, Gödel relabelling, Heisenberg–Weyl algebra
Citação
FRANCISCO 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.