A Rigorous Derivation of the Functional Renormalisation Group Equation
arXiv:2106.09466 · doi:10.1007/s00220-023-04821-7
Abstract
The functional renormalisation group equation is derived in a mathematically rigorous fashion in a framework suitable for the Osterwalder-Schrader formulation of quantum field theory. To this end, we devise a very general regularisation scheme which retains reflection positivity as well as the infinite degrees of freedom including smoothness. Furthermore, it is shown how the classical limit is altered by the regularisation process leading to an inevitable breaking of translation invariance. We also give precise conditions for the convergence of the obtained theories upon removal of the regularisation.
References in corpus (10)
- Exact evolution equation for the effective potential
- New Measurement of the Electron Magnetic Moment and the Fine Structure Constant
- The Exact Renormalisation Group and Approximate Solutions
- The nonperturbative functional renormalization group and its applications
- An Introduction to the Nonperturbative Renormalization Group
- Introduction to the functional RG and applications to gauge theories
- Flow Equations for N Point Functions and Bound States
- Proton Mass Decomposition from the QCD Energy Momentum Tensor
- Existence and Construction of Exact FRG Flows of a UV-Interacting Scalar Field Theory
- Super-Gaussian Decay of Exponentials: A Sufficient Condition