Renormalizability of the Schr\"odinger Functional

TL;DR

This paper proves that the Schr"odinger functional in quantum field theory with boundaries can be renormalized to all orders by adjusting surface interaction coefficients, ensuring consistent quantum predictions.

Contribution

It demonstrates the all-order renormalizability of surface interactions in the Schr"odinger functional framework, extending Symanzik's boundary condition formulation.

Findings

Surface divergences can be absorbed by coefficient renormalization.

Renormalization applies to all orders in perturbation theory.

Supports consistent quantum field theory with boundaries.

Abstract

Symanzik showed that quantum field theory can be formulated on a space with boundaries by including suitable surface interactions in the action to implement boundary conditions. We show that to all orders in perturbation theory all the divergences induced by these surface interactions can be absorbed by a renormalization of their coefficients.