AG Mathematische Physik, Ko Sanders (FAU): Quantum energy inequalities and their applications

Ko Sanders (FAU)

Quantum energy inequalities and their applications

Abstract:
Quantum energy inequalities can be used to express the stability of
a quantum field theory in analogy to the classical energy conditions
in GR. In particular, they are expected to be a suitable assumption
to prove quantum analogs of e.g. the classical singularity theorems
of Penrose and Hawking, where energy conditions played a key role.
After a brief general review of these quantum energy inequalities, I
will argue that they also have another important application: they
can be used to control the high energy behaviour of quantum fields.
This is in analogy to Hamiltonian bounds for quantum fields in
Minkowski space, replacing the Hamiltonian operator by an averaged
energy density. This potentially opens up the way to manipulate
pointwise quantum fields and operator product expansions in a
rigorous way, also for quantum fields in curved spacetimes, where
in general no Hamiltonian operator is available.