Perturbative Renormalisation for Not-Quite-Connected Bialgebras

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Perturbative Renormalisation for Not-Quite-Connected Bialgebras. / Kock, Joachim.

In: Letters in Mathematical Physics, Vol. 105, No. 10, 10.2015, p. 1413-1425.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Kock, J 2015, 'Perturbative Renormalisation for Not-Quite-Connected Bialgebras', Letters in Mathematical Physics, vol. 105, no. 10, pp. 1413-1425. https://doi.org/10.1007/s11005-015-0785-7

APA

Kock, J. (2015). Perturbative Renormalisation for Not-Quite-Connected Bialgebras. Letters in Mathematical Physics, 105(10), 1413-1425. https://doi.org/10.1007/s11005-015-0785-7

Vancouver

Kock J. Perturbative Renormalisation for Not-Quite-Connected Bialgebras. Letters in Mathematical Physics. 2015 Oct;105(10):1413-1425. https://doi.org/10.1007/s11005-015-0785-7

Author

Kock, Joachim. / Perturbative Renormalisation for Not-Quite-Connected Bialgebras. In: Letters in Mathematical Physics. 2015 ; Vol. 105, No. 10. pp. 1413-1425.

Bibtex

@article{90862ca27f61448aa2a9906c763443ba,
title = "Perturbative Renormalisation for Not-Quite-Connected Bialgebras",
abstract = "We observe that the Connes-Kreimer Hopf-algebraic approach to perturbative renormalisation works not just for Hopf algebras but more generally for filtered bialgebras B with the property that B (0) is spanned by group-like elements (e.g. pointed bialgebras with the coradical filtration). Such bialgebras occur naturally both in quantum field theory, where they have some attractive features, and elsewhere in combinatorics, where they cover a comprehensive class of incidence bialgebras. In particular, the setting allows us to interpret Mobius inversion as an instance of renormalisation.",
keywords = "perturbative renormalisation, bialgebras, DYSON-SCHWINGER EQUATIONS, HOPF-ALGEBRAS, FEYNMAN GRAPHS, TREES",
author = "Joachim Kock",
year = "2015",
month = oct,
doi = "10.1007/s11005-015-0785-7",
language = "English",
volume = "105",
pages = "1413--1425",
journal = "Letters in Mathematical Physics",
issn = "0377-9017",
publisher = "Springer",
number = "10",

}

RIS

TY - JOUR

T1 - Perturbative Renormalisation for Not-Quite-Connected Bialgebras

AU - Kock, Joachim

PY - 2015/10

Y1 - 2015/10

N2 - We observe that the Connes-Kreimer Hopf-algebraic approach to perturbative renormalisation works not just for Hopf algebras but more generally for filtered bialgebras B with the property that B (0) is spanned by group-like elements (e.g. pointed bialgebras with the coradical filtration). Such bialgebras occur naturally both in quantum field theory, where they have some attractive features, and elsewhere in combinatorics, where they cover a comprehensive class of incidence bialgebras. In particular, the setting allows us to interpret Mobius inversion as an instance of renormalisation.

AB - We observe that the Connes-Kreimer Hopf-algebraic approach to perturbative renormalisation works not just for Hopf algebras but more generally for filtered bialgebras B with the property that B (0) is spanned by group-like elements (e.g. pointed bialgebras with the coradical filtration). Such bialgebras occur naturally both in quantum field theory, where they have some attractive features, and elsewhere in combinatorics, where they cover a comprehensive class of incidence bialgebras. In particular, the setting allows us to interpret Mobius inversion as an instance of renormalisation.

KW - perturbative renormalisation

KW - bialgebras

KW - DYSON-SCHWINGER EQUATIONS

KW - HOPF-ALGEBRAS

KW - FEYNMAN GRAPHS

KW - TREES

U2 - 10.1007/s11005-015-0785-7

DO - 10.1007/s11005-015-0785-7

M3 - Journal article

VL - 105

SP - 1413

EP - 1425

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 10

ER -

ID: 331498927