The c and a-Theorems and the Local Renormalisation Group

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, Quantum Theory
Cover of the book The c and a-Theorems and the Local Renormalisation Group by Graham Shore, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Graham Shore ISBN: 9783319540009
Publisher: Springer International Publishing Publication: March 30, 2017
Imprint: Springer Language: English
Author: Graham Shore
ISBN: 9783319540009
Publisher: Springer International Publishing
Publication: March 30, 2017
Imprint: Springer
Language: English

The 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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

The 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.

More books from Springer International Publishing

Cover of the book Aesthetic Septorhinoplasty by Graham Shore
Cover of the book Health Risks and Fair Compensation in the Fire Service by Graham Shore
Cover of the book The British General Election of 2017 by Graham Shore
Cover of the book Advanced High Strength Sheet Steels by Graham Shore
Cover of the book Liquid Crystal Colloids by Graham Shore
Cover of the book Carl von Clausewitz, the Fog-of-War, and the AI Revolution by Graham Shore
Cover of the book Biotechnology of Extremophiles: by Graham Shore
Cover of the book Functional Ophthalmic Disorders by Graham Shore
Cover of the book The Form of Poetry in the 1820s and 1830s by Graham Shore
Cover of the book Information Security Education Across the Curriculum by Graham Shore
Cover of the book Food Parcels in International Migration by Graham Shore
Cover of the book The Neurobiological Basis of Memory by Graham Shore
Cover of the book Memory as Colonial Capital by Graham Shore
Cover of the book Smart Cities in the Mediterranean by Graham Shore
Cover of the book Applications in Electronics Pervading Industry, Environment and Society by Graham Shore
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy