Cite as: doi:10.26081/K69K75

**
A generic burst of classical gravitational radiation will cause an array of
freely falling test masses far from the source to experience a permanent
displacement, called the "Gravitational Memory Effect". This effect is
responsible for the, previously unexpected, enlargement of the asymptotic
symmetry group from the usual Poincar Group to the BMS group. Furthermore,
Memory (and its field theory analogs) are responsible for all infrared
divergences in any formulation of Quantum Gravity as well as in Quantum Field
Theory. Hilbert spaces containing states with differing Memories are unitarily
inequivalent to each other and, consequently, "out" scattering states live in an
uncountably infinite set of unitarily inequivalent Hilbert spaces (one for each
Memory). The longstanding "infrared problem" is the construction of an
"IR-finite" S-matrix by constructing "in" and "out" Hilbert spaces which (1)
includes states with Memory, (2) is separable and (3) unitarily implements the
BMS group. In this talk, I will describe these classical and quantum connections
from a geometric and intuitive perspective. I will then clarify that while there
is an essentially unique construction of such a Hilbert space in QFT using known
as "Faddeev Kulish dressing", this construction cannot be applied to Quantum
Gravity. In Quantum Gravity, we prove that conditions (1) and (2) imply that the
Hilbert space is a Direct Integral (a generalization of the Direct sum) with
some choice of infinite-dimensional measure on the space of Memories. We prove
new constraints on the space of allowed Memories and that there are no BMS
invariant Gaussian measures which satisfy these constraints. In totality, our
results suggest that the "in" and "out" states are more appropriately described
in the Algebraic framework. I conclude by commenting on the implications of our
results for recent holographic proposals.
**

**
**

To download: Right-click and choose "Save Link As..."