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http://www.repositorio.ufop.br/jspui/handle/123456789/8732
Título: | Matula numbers, Gödel numbering and Fock space. |
Autor(es): | Francisco Neto, Antônio |
Palavras-chave: | Rooted trees Hopf algebra Gödel relabelling Heisenberg–Weyl algebra |
Data do documento: | 2013 |
Referência: | 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. |
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). |
URI: | http://www.repositorio.ufop.br/handle/123456789/8732 |
Link para o artigo: | https://link.springer.com/article/10.1007/s10910-013-0178-z |
DOI: | https://doi.org/10.1007/s10910-013-0178-z |
ISSN: | 1572-8897 |
Aparece nas coleções: | DEPRO - Artigos publicados em periódicos |
Arquivos associados a este item:
Arquivo | Descrição | Tamanho | Formato | |
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ARTIGO_MatulaNumberGödel.pdf Restricted Access | 469,47 kB | Adobe PDF | Visualizar/Abrir |
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