**algebraic quantum field theory** (perturbative, on curved spacetimes, homotopical)

**quantum mechanical system**, **quantum probability**

**interacting field quantization**

In perturbative quantum field theory generally all quantum observables are subject to renormalization choices that may change their value from that computed in classical field theory. But if renormalization conditions are imposed, these generally reduce the space of renormalization choices. If a choice of renormalization condition completely removes the renormalization freedom in an observable, one says that it *protects* the observable from *receiving quantum corrections*.

Typically this is considered for global symmetries, the renormalization condition being that the symmetry is retained after renormalization. In this case one says that that the *symmetry protects* the quantum observable from receiving quantum corrections.

Famous examples of protected quantities are masses and charges of BPS-states, which are protected, in this way, by supersymmetry. The reason why supersymmetric field theory admits more interesting computations than are possible otherwise is that the protection of BPS states allows to compute many quantum observables that would otherwise not be computatble in practice.

This is for instance the reason why so much is known about the Bekenstein-Hawking entropy of extremal (hence BPS) black holes (see at *black holes in string theory*) while comparatively little is known about the quantum properties of non-BPS and hence “non-protected” black holes.

Last revised on July 18, 2024 at 12:45:12. See the history of this page for a list of all contributions to it.