The Resource The c and aTheorems and the Local Renormalisation Group, by Graham Shore, (electronic resource)
The c and aTheorems and the Local Renormalisation Group, by Graham Shore, (electronic resource)
 Summary
 The Zamolodchikov ctheorem has led to important new insights in the understanding of the Renormalisation Group (RG) and the geometry of the space of QFTs. The present primer introduces and reviews the parallel developments of the search for a higherdimensional generalisation of the ctheorem and of the Local RG (LRG). The idea of renormalisation with positiondependent couplings, running under local Weyl scaling, is traced from its early realisations to the elegant modern formalism of the LRG. The key rôle of the associated Weyl consistency conditions in establishing RG flow equations for the coefficients of the trace anomaly in curved spacetime, and their relation to the ctheorem and fourdimensional atheorem, is explained in detail. A number of different derivations of the ctheorem in two dimensions are presented and subsequently generalised to four dimensions. The obstructions to establishing monotonic Cfunctions related to the trace anomaly coefficients in four dimensions are explained. The possibility of deriving an atheorem for the coefficient of the EulerGaussBonnet density is explored, initially by formulating the QFT on maximally symmetric spaces. Then the formulation of the weak atheorem using a dispersion relation for fourpoint functions is presented. Finally, the application of the LRG to the issue of limit cycles in theories with a global symmetry is described, shedding new light on the geometry of the space of couplings in QFT
 Language
 eng
 Extent
 VII, 102 p. 5 illus., 3 illus. in color.
 Contents

 Introduction
 Renormalisation and the Conformal Anomaly
 The Local Renormalisation Group and Weyl Consistency Conditions
 cTheorem in Two Dimensions
 Local RGE and Weyl Consistency Conditions in Four Dimensions
 c, b and aTheorems in Four Dimensions
 Global Symmetries and Limit Cycles
 Summary and Outlook
 Isbn
 9783319540009
 Label
 The c and aTheorems and the Local Renormalisation Group
 Title
 The c and aTheorems and the Local Renormalisation Group
 Statement of responsibility
 by Graham Shore
 Language
 eng
 Summary
 The Zamolodchikov ctheorem has led to important new insights in the understanding of the Renormalisation Group (RG) and the geometry of the space of QFTs. The present primer introduces and reviews the parallel developments of the search for a higherdimensional generalisation of the ctheorem and of the Local RG (LRG). The idea of renormalisation with positiondependent couplings, running under local Weyl scaling, is traced from its early realisations to the elegant modern formalism of the LRG. The key rôle of the associated Weyl consistency conditions in establishing RG flow equations for the coefficients of the trace anomaly in curved spacetime, and their relation to the ctheorem and fourdimensional atheorem, is explained in detail. A number of different derivations of the ctheorem in two dimensions are presented and subsequently generalised to four dimensions. The obstructions to establishing monotonic Cfunctions related to the trace anomaly coefficients in four dimensions are explained. The possibility of deriving an atheorem for the coefficient of the EulerGaussBonnet density is explored, initially by formulating the QFT on maximally symmetric spaces. Then the formulation of the weak atheorem using a dispersion relation for fourpoint functions is presented. Finally, the application of the LRG to the issue of limit cycles in theories with a global symmetry is described, shedding new light on the geometry of the space of couplings in QFT
 Image bit depth
 0
 Literary form
 non fiction
 Series statement
 SpringerBriefs in Physics,
 Label
 The c and aTheorems and the Local Renormalisation Group, by Graham Shore, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction  Renormalisation and the Conformal Anomaly  The Local Renormalisation Group and Weyl Consistency Conditions  cTheorem in Two Dimensions  Local RGE and Weyl Consistency Conditions in Four Dimensions  c, b and aTheorems in Four Dimensions  Global Symmetries and Limit Cycles  Summary and Outlook
 http://library.link/vocab/cover_art
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 unknown
 http://library.link/vocab/discovery_link
 {'f': 'http://opac.lib.rpi.edu/record=b4257869'}
 Extent
 VII, 102 p. 5 illus., 3 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319540009
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other physical details
 online resource.
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.lib.rpi.edu/portal/ThecandaTheoremsandtheLocal/gFzh2CYFylg/" typeof="WorkExample http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.lib.rpi.edu/portal/ThecandaTheoremsandtheLocal/gFzh2CYFylg/">The c and aTheorems and the Local Renormalisation Group, by Graham Shore, (electronic resource)</a></span>  <span property="offers" typeOf="Offer"><span property="offeredBy" typeof="Library ll:Library" resource="http://link.lib.rpi.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.lib.rpi.edu/">Rensselaer Libraries</a></span></span></span></span></div>