From Mobius inversion to renormalisation

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From Mobius inversion to renormalisation. / Kock, Joachim.

In: Communications in Number Theory and Physics, Vol. 14, No. 1, 2020, p. 171-198.

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

Harvard

Kock, J 2020, 'From Mobius inversion to renormalisation', Communications in Number Theory and Physics, vol. 14, no. 1, pp. 171-198.

APA

Kock, J. (2020). From Mobius inversion to renormalisation. Communications in Number Theory and Physics, 14(1), 171-198.

Vancouver

Kock J. From Mobius inversion to renormalisation. Communications in Number Theory and Physics. 2020;14(1):171-198.

Author

Kock, Joachim. / From Mobius inversion to renormalisation. In: Communications in Number Theory and Physics. 2020 ; Vol. 14, No. 1. pp. 171-198.

Bibtex

@article{ef1fa4a2ee714889aeabd733e0b668a0,
title = "From Mobius inversion to renormalisation",
abstract = "This paper traces a straight line from classical Mobius inversion to Hopf-algebraic perturbative renormalisation. This line, which is logical but not entirely historical, consists of just a few main abstraction steps, and some intermediate steps dwelled upon for mathematical pleasure. The paper is largely expository, but contains many new perspectives on well-known results. For example, the equivalence between the Bogoliubov recursion and the Atkinson formula is exhibited as a direct generalisation of the equivalence between the Weisner-Rota recursion and the Hall-Leroux formula for Mobius inversion.",
keywords = "Mobius inversion, perturbative renormalisation, bialgebras, coalgebras, ROTA-BAXTER ALGEBRAS, QUANTUM-FIELD THEORY, HOPF-ALGEBRAS",
author = "Joachim Kock",
year = "2020",
language = "English",
volume = "14",
pages = "171--198",
journal = "Communications in Number Theory and Physics",
issn = "1931-4523",
publisher = "International Press of Boston, Inc.",
number = "1",

}

RIS

TY - JOUR

T1 - From Mobius inversion to renormalisation

AU - Kock, Joachim

PY - 2020

Y1 - 2020

N2 - This paper traces a straight line from classical Mobius inversion to Hopf-algebraic perturbative renormalisation. This line, which is logical but not entirely historical, consists of just a few main abstraction steps, and some intermediate steps dwelled upon for mathematical pleasure. The paper is largely expository, but contains many new perspectives on well-known results. For example, the equivalence between the Bogoliubov recursion and the Atkinson formula is exhibited as a direct generalisation of the equivalence between the Weisner-Rota recursion and the Hall-Leroux formula for Mobius inversion.

AB - This paper traces a straight line from classical Mobius inversion to Hopf-algebraic perturbative renormalisation. This line, which is logical but not entirely historical, consists of just a few main abstraction steps, and some intermediate steps dwelled upon for mathematical pleasure. The paper is largely expository, but contains many new perspectives on well-known results. For example, the equivalence between the Bogoliubov recursion and the Atkinson formula is exhibited as a direct generalisation of the equivalence between the Weisner-Rota recursion and the Hall-Leroux formula for Mobius inversion.

KW - Mobius inversion

KW - perturbative renormalisation

KW - bialgebras

KW - coalgebras

KW - ROTA-BAXTER ALGEBRAS

KW - QUANTUM-FIELD THEORY

KW - HOPF-ALGEBRAS

M3 - Journal article

VL - 14

SP - 171

EP - 198

JO - Communications in Number Theory and Physics

JF - Communications in Number Theory and Physics

SN - 1931-4523

IS - 1

ER -

ID: 331497812