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000780597 019__ $$a981672143$$a981896279$$a984868781
000780597 020__ $$a9783319540009$$q(electronic book)
000780597 020__ $$a3319540009$$q(electronic book)
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000780597 0247_ $$a10.1007/978-3-319-54000-9$$2doi
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000780597 08204 $$a530.15$$223
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000780597 1001_ $$aShore, Graham,$$eauthor.
000780597 24514 $$aThe c and a-Theorems and the local renormalisation group /$$cGraham Shore.
000780597 264_1 $$aCham, Switzerland :$$bSpringer,$$c2017.
000780597 300__ $$a1 online resource (vii, 102 pages) :$$billustrations).
000780597 336__ $$atext$$btxt$$2rdacontent
000780597 337__ $$acomputer$$bc$$2rdamedia
000780597 338__ $$aonline resource$$bcr$$2rdacarrier
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000780597 4901_ $$aSpringerBriefs in physics
000780597 504__ $$aIncludes bibliographical references.
000780597 5050_ $$aAbstract; 1 Introduction; 1.1 Scale, Conformal and Weyl Invariance; 1.2 Renormalisation Group Flows and the Zamolodchikovc-Theorem; 1.3 Local Renormalisation Group; 2 Renormalisation and the Conformal Anomaly; 2.1 Renormalisation and Local Couplings; 2.2 Trace Anomaly; 2.3 Renormalisation of Two-Point Green Functions; 3 The Local Renormalisation Group and WeylConsistency Conditions; 3.1 Diffeomorphism and Anomalous Weyl Ward Identities; 3.2 Renormalisation Group and Green Functions; 3.3 Weyl Consistency Conditions; 3.4 Local RGE and Weyl Consistency Conditions
000780597 5058_ $$a4 c-Theorem in Two Dimensions4.1 c-Theorem and the Spectral Function ; 4.2 c-Theorem and Renormalisation Group Flow; 4.3 c-Theorem in Position Space; 4.4 c-Theorem and Dispersion Relations; 5 Local RGE and Weyl Consistency Conditions in Four Dimensions; 5.1 Local RGE, Trace Anomaly and Weyl Consistency Conditions; 5.2 Renormalisation Group and Anomalous Ward Identities for Green Functions; 5.3 Weyl Consistency Conditions; 6 c, b and a-Theorems in Four Dimensions; 6.1 Spectral Functions and the c and b 'Theorems'; 6.2 Renormalisation Group Flow for the c and b 'Theorems'
000780597 5058_ $$a6.3 Weyl Consistency Conditions and the a-Theorem7 Local RGE and Maximally Symmetric Spaces; 7.1 Renormalisation Group, Weyl Consistency Conditions and the a-Theorem; 7.2 RG Flow of on Maximally Symmetric Spaces; 7.3 Zamolodchikov Functions and the Search for a C-Theorem on the Sphere; 7.3.1 Geometry of Constant Curvature Spaces; 7.3.2 Two-Point Green Functions and Conservation Identities; 7.3.3 The Zamolodchikov C-Function on the Sphere; 7.3.4 Dimensional Analysis and RG Flow of the C-Function; 8 The Weak a-Theorem and 4-Point Green Functions; 9 Global Symmetries and Limit Cycles
000780597 5058_ $$a9.1 Global Symmetries and Weyl Consistency Conditions9.2 Limit Cycles; 10 Summary and Outlook; A Counterterms for Renormalised Green Functions; B RGEs for Two-Point Green Functions; C Zamolodchikov Functions in n Dimensions; References
000780597 506__ $$aAccess limited to authorized users.
000780597 520__ $$aThe Zamolodchikov c-theorem has led to important new insights in the understanding of the Renormalisation Group (RG) and the geometry of the space of QFTs. The present primer introduces and reviews the parallel developments of the search for a higher-dimensional generalisation of the c-theorem and of the Local RG (LRG). The idea of renormalisation with position-dependent couplings, running under local Weyl scaling, is traced from its early realisations to the elegant modern formalism of the LRG. The key rôle of the associated Weyl consistency conditions in establishing RG flow equations for the coefficients of the trace anomaly in curved spacetime, and their relation to the c-theorem and four-dimensional a-theorem, is explained in detail. A number of different derivations of the c-theorem in two dimensions are presented and subsequently generalised to four dimensions. The obstructions to establishing monotonic C-functions related to the trace anomaly coefficients in four dimensions are explained. The possibility of deriving an a-theorem for the coefficient of the Euler-Gauss-Bonnet density is explored, initially by formulating the QFT on maximally symmetric spaces. Then the formulation of the weak a-theorem using a dispersion relation for four-point functions is presented. Finally, the application of the LRG to the issue of limit cycles in theories with a global symmetry is described, shedding new light on the geometry of the space of couplings in QFT.
000780597 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed April 11, 2017).
000780597 650_0 $$aRenormalization group.
000780597 650_0 $$aMathematical physics.
000780597 77608 $$iPrint version:$$z9783319539997$$z331953999X$$w(OCoLC)969829800
000780597 830_0 $$aSpringerBriefs in physics.
000780597 852__ $$bebk
000780597 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-54000-9$$zOnline Access$$91397441.1
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