2017/02/28 by Javier M. Lizana, J. M. Lizana, M. Perez-Victoria +1 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Correlation function (quantum field theory) #Cosmology and Gravitation Theories #Cutoff #Formalism (music) #Gaussian #Mathematical physics #Mathematics #Physics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Scalar (mathematics) #hep-ph #hep-th
paper · pdf · doi:10.1007/jhep06(2017)139
40 pages, 2 figures. Minor changes and references added. Matches JHEP version
openalex publication_date 2017/06/01 · arxiv created 2018/05/07 · arxiv updated 2018/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We examine the precise connection between the exact renormalisation group with local couplings and the renormalisation of correlation functions of composite operators in scale-invariant theories. A geometric description of theory space allows us to select convenient non-linear parametrisations that serve different purposes. First, we identify normal parameters in which the renormalisation group flows take their simplest form; normal correlators are defined by functional differentiation with respect to these parameters. The renormalised correlation functions are given by the continuum limit of correlators associated to a cutoff-dependent parametrisation, which can be related to the renormalisation group flows. The necessary linear and non-linear counterterms in any arbitrary parametrisation arise in a natural way from a change of coordinates. We show that, in a class of minimal subtraction schemes, the renormalised correlators are exactly equal to normal correlators evaluated at a finite cutoff. To illustrate the formalism and the main results, we compare standard diagrammatic calculations in a scalar free-field theory with the structure of the perturbative solutions to the Polchinski equation close to the Gaussian fixed point.