Counting paths with Schur transitions
| Autor: | Alvaro Veliz-Osorio, Pablo Diaz, Garreth Kemp |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
High Energy Physics - Theory
Physics Nuclear and High Energy Physics Pure mathematics Unitarity 010308 nuclear & particles physics Branching fraction FOS: Physical sciences Mathematical Physics (math-ph) Relative dimension 01 natural sciences Graph Formal proof High Energy Physics - Theory (hep-th) Quantum mechanics Unitary group 0103 physical sciences lcsh:QC770-798 lcsh:Nuclear and particle physics. Atomic energy. Radioactivity 010306 general physics General validity Quantum Mathematical Physics |
| Zdroj: | Nuclear Physics B Nuclear Physics B, Vol 911, Iss C, Pp 295-317 (2016) |
| Popis: | In this work we explore the structure of the branching graph of the unitary group using Schur transitions. We find that these transitions suggest a new combinatorial expression for counting paths in the branching graph. This formula, which is valid for any rank of the unitary group, reproduces known asymptotic results. We proceed to establish the general validity of this expression by a formal proof. The form of this equation strongly hints towards a quantum generalization. Thus, we introduce a notion of quantum relative dimension and subject it to the appropriate consistency tests. This new quantity finds its natural environment in the context of RCFTs and fractional statistics; where the already established notion of quantum dimension has proven to be of great physical importance. Comment: 30 pages, 5 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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