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Gravity Theory Seminar

Date
Thu, Aug 5, 2021 3:00 pm - 4:00 pm
Location
PSC 3150

Description

Speaker: Rodrigo Andrade E Silva

Title: Quantization of a causal diamond in 2+1 dimensional gravity

Abstract: We develop the reduced phase space quantization of causal
diamonds in pure 2+1 dimensional gravity with a negative
cosmological constant. The system is defined as the domain
of dependence of a spacelike topological disk with fixed
boundary length. By solving the constraints in a
constant-mean-curvature time gauge and removing all the
spatial gauge redundancy, we find that the phase space is
the cotangent bundle of Diff^+(S^1)/PSL(2, R). To quantize
this nonlinear phase space we apply Isham's group-theoretic
quantization scheme, and find that the quantum theory can be
realized by wavefunctions on some coadjoint orbit of the
Virasoro group, with labels in irreducible unitary
representations of the corresponding little group. We find
that the twist of the diamond boundary loop is quantized in
terms of the ratio of the Planck length to the boundary
length.