On the interplay between boundary conditions and the Lorentzian Wetterich equation
arxiv(2024)
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 à 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 Poincaré 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.
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