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Exact scheme independence at two loops

Exact scheme independence at two loops
Exact scheme independence at two loops
We further develop an algorithmic and diagrammatic computational framework for very general exact renormalization groups, where the embedded regularisation scheme, parametrised by a general cutoff function and infinitely many higher point vertices, is left unspecified. Calculations proceed iteratively, by integrating by parts with respect to the effective cutoff, thus introducing effective propagators, and differentials of vertices that can be expanded using the flow equations; many cancellations occur on using the fact that the effective propagator is the inverse of the classical Wilsonian two-point vertex. We demonstrate the power of these methods by computing the beta function up to two loops in massless four dimensional scalar field theory, obtaining the expected universal coefficients, independent of the details of the regularisation scheme.
renormalisation, vertex functions
1550-7998
065009-[13pp]
Arnone, Stefano
d2a9a0a5-34fd-4205-b5f4-107208f44fb2
Gatti, Antonio
ca881118-1418-49bc-98eb-23f315d96d59
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Rosten, Oliver J.
26ca1633-a7c7-418f-af0d-e65b4ec487ed
Arnone, Stefano
d2a9a0a5-34fd-4205-b5f4-107208f44fb2
Gatti, Antonio
ca881118-1418-49bc-98eb-23f315d96d59
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Rosten, Oliver J.
26ca1633-a7c7-418f-af0d-e65b4ec487ed

Arnone, Stefano, Gatti, Antonio, Morris, Tim R. and Rosten, Oliver J. (2004) Exact scheme independence at two loops. Physical Review D, 69 (6), 065009-[13pp]. (doi:10.1103/PhysRevD.69.065009).

Record type: Article

Abstract

We further develop an algorithmic and diagrammatic computational framework for very general exact renormalization groups, where the embedded regularisation scheme, parametrised by a general cutoff function and infinitely many higher point vertices, is left unspecified. Calculations proceed iteratively, by integrating by parts with respect to the effective cutoff, thus introducing effective propagators, and differentials of vertices that can be expanded using the flow equations; many cancellations occur on using the fact that the effective propagator is the inverse of the classical Wilsonian two-point vertex. We demonstrate the power of these methods by computing the beta function up to two loops in massless four dimensional scalar field theory, obtaining the expected universal coefficients, independent of the details of the regularisation scheme.

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More information

Published date: 2004
Keywords: renormalisation, vertex functions

Identifiers

Local EPrints ID: 12460
URI: http://eprints.soton.ac.uk/id/eprint/12460
ISSN: 1550-7998
PURE UUID: 4ae05b71-1fea-4a7f-9c70-e40951c5f0e3
ORCID for Tim R. Morris: ORCID iD orcid.org/0000-0001-6256-9962

Catalogue record

Date deposited: 08 May 2006
Last modified: 22 Jun 2021 01:32

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