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Dostęp zamkniętyA ribbon graph derivation of the algebra of functional renormalization for random multi-matrices with multi-trace interactions
| cris.lastimport.scopus | 2024-02-12T20:06:45Z |
| dc.abstract.en | We focus on functional renormalization for ensembles of several (say n≥1) random matrices, whose potentials include multi-traces, to wit, the probability measure contains factors of the form exp[−Tr(V1)×⋯×Tr(Vk)] for certain noncommutative polynomials V1,…,Vk∈C⟨n⟩ in the n matrices. This article shows how the “algebra of functional renormalization” – that is, the structure that makes the renormalization flow equation computable – is derived from ribbon graphs, only by requiring the one-loop structure that such equation (due to Wetterich) is expected to have. Whenever it is possible to compute the renormalization flow in terms of U(N)-invariants, the structure gained is the matrix algebra M_n(A,⋆) with entries in A=(C⟨n⟩⊗C⟨n⟩)⊕(C⟨n⟩⊠C⟨n⟩), being C⟨n⟩ the free algebra generated by the n Hermitian matrices of size N (the flowing random variables) with multiplication of homogeneous elements in An,N given, for each P,Q,U,W∈C⟨n⟩, by (U⊗W)⋆(P⊗Q)=PU⊗WQ,(U⊠W)⋆(P⊗Q)=U⊠PWQ,(U⊗W)⋆(P⊠Q)=WPU⊠Q,(U⊠W)⋆(P⊠Q)=Tr(WP)U⊠Q, which, together with the condition (λU)⊠W=U⊠(λW) for each complex λ, fully define the symbol ⊠. |
| dc.affiliation | Uniwersytet Warszawski |
| dc.contributor.author | Sanchez, Carlos Ignacio Perez |
| dc.date.accessioned | 2024-01-24T18:06:40Z |
| dc.date.available | 2024-01-24T18:06:40Z |
| dc.date.issued | 2022 |
| dc.description.finance | Publikacja bezkosztowa |
| dc.description.number | 58 |
| dc.description.volume | 112 |
| dc.identifier.doi | 10.1007/S11005-022-01546-X |
| dc.identifier.issn | 0377-9017 |
| dc.identifier.uri | https://repozytorium.uw.edu.pl//handle/item/101842 |
| dc.language | eng |
| dc.pbn.affiliation | physical sciences |
| dc.relation.ispartof | Letters in Mathematical Physics |
| dc.rights | ClosedAccess |
| dc.sciencecloud | nosend |
| dc.title | A ribbon graph derivation of the algebra of functional renormalization for random multi-matrices with multi-trace interactions |
| dc.type | JournalArticle |
| dspace.entity.type | Publication |