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Derivative expansion of the exact renormalization group

The functional flow equations for the Legendre effective action, with respect to changes in a smooth cutoff, are approximated by a derivative expansion; no other approximation is made. This results in a set of coupled non-linear differential equations. The corresponding differential equations for a...

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Autor principal: Morris, Tim R.
Lenguaje:eng
Publicado: 1994
Materias:
Acceso en línea:https://dx.doi.org/10.1016/0370-2693(94)90767-6
http://cds.cern.ch/record/260759
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author Morris, Tim R.
author_facet Morris, Tim R.
author_sort Morris, Tim R.
collection CERN
description The functional flow equations for the Legendre effective action, with respect to changes in a smooth cutoff, are approximated by a derivative expansion; no other approximation is made. This results in a set of coupled non-linear differential equations. The corresponding differential equations for a fixed point action have at most a countable number of solutions that are well defined for all values of the field. We apply the technique to the fixed points of one-component real scalar field theory in three dimensions. Only two non-singular solutions are found: the gaussian fixed point and an approximation to the Wilson fixed point. The latter is used to compute critical exponents, by carrying the approximation to second order. The results appear to converge rapidly.
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institution Organización Europea para la Investigación Nuclear
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publishDate 1994
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spelling cern-2607592023-10-04T07:44:52Zdoi:10.1016/0370-2693(94)90767-6http://cds.cern.ch/record/260759engMorris, Tim R.Derivative expansion of the exact renormalization groupGeneral Theoretical PhysicsThe functional flow equations for the Legendre effective action, with respect to changes in a smooth cutoff, are approximated by a derivative expansion; no other approximation is made. This results in a set of coupled non-linear differential equations. The corresponding differential equations for a fixed point action have at most a countable number of solutions that are well defined for all values of the field. We apply the technique to the fixed points of one-component real scalar field theory in three dimensions. Only two non-singular solutions are found: the gaussian fixed point and an approximation to the Wilson fixed point. The latter is used to compute critical exponents, by carrying the approximation to second order. The results appear to converge rapidly.The functional flow equations for the Legendre effective action, with respect to changes in a smooth cutoff, are approximated by a derivative expansion; no other approximation is made. This results in a set of coupled non-linear differential equations. The corresponding differential equations for a fixed point action have at most a countable number of solutions that are well defined for all values of the field. We apply the technique to the fixed points of one-component real scalar field theory in three dimensions. Only two non-singular solutions are found: the gaussian fixed point and an approximation to the Wilson fixed point. The latter is used to compute critical exponents, by carrying the approximation to second order. The results appear to converge rapidly.The functional flow equations for the Legendre effective action, with respect to changes in a smooth cutoff, are approximited by a derivative expansion; no other approximation is made. This results in a set of coupled non-linear differential equations. The corresponding differential equations for a fixed point action have at most a countable number of solutions that are well defined for all values of the field. We apply the technique to the fixed points of one-component real scalar field theory in three dimensions. Only two non-singular solutions are found; the gaussian fixed point and an approximation to the Wilson fixed point. The latter is used to compute critical exponents, by carrying the approximation to second order. The results appear to converge rapidly.hep-ph/9403340CERN-TH-7203-94SHEP-93-94-16CERN-TH-7203-94SHEP-93-94-16oai:cds.cern.ch:2607591994
spellingShingle General Theoretical Physics
Morris, Tim R.
Derivative expansion of the exact renormalization group
title Derivative expansion of the exact renormalization group
title_full Derivative expansion of the exact renormalization group
title_fullStr Derivative expansion of the exact renormalization group
title_full_unstemmed Derivative expansion of the exact renormalization group
title_short Derivative expansion of the exact renormalization group
title_sort derivative expansion of the exact renormalization group
topic General Theoretical Physics
url https://dx.doi.org/10.1016/0370-2693(94)90767-6
http://cds.cern.ch/record/260759
work_keys_str_mv AT morristimr derivativeexpansionoftheexactrenormalizationgroup