On the interplay between boundary conditions and the Lorentzian Wetterich equation
Abstract
In the framework of the functional renormalization group and of the perturbative, algebraic approach to quantum field theory (pAQFT), in [DDPR23] it has been derived a Lorentian version of a flow equation \`a la Wetterich, which can be used to study non linear, quantum scalar field theories on a globally hyperbolic spacetime. In this work we show that the realm of validity of this result can be extended to study interacting scalar field theories on globally hyperbolic manifolds with a timelike boundary. By considering the specific examples of half Minkowski spacetime and of the Poincar\'e patch of Anti-de Sitter, we show that the form of the Lorentzian Wetterich equation is strongly dependent on the boundary conditions assigned to the underlying field theory. In addition, using a numerical approach, we are able to provide strong evidences that there is a qualitative and not only a quantitative difference in the associated flow and we highlight this feature by considering Dirichlet and Neumann boundary conditions on half Minkowski spacetime.
Keywords
Cite
@article{arxiv.2401.07130,
title = {On the interplay between boundary conditions and the Lorentzian Wetterich equation},
author = {Claudio Dappiaggi and Filippo Nava and Luca Sinibaldi},
journal= {arXiv preprint arXiv:2401.07130},
year = {2024}
}
Comments
38 pages, 23 figures