Causal diamonds in 2+1 dimensional quantum gravity

Abstract: We identify the reduced phase space of causal diamonds with fixed edge length in pure 2+1 dimensional gravity with a negative cosmological constant, which turns out to be the cotangent bundle of the homogeneous space $Diff^+(S^1)/PSL(2,R)$. Isham’s group theoretic quantization scheme is applied to this nonlinear phase space. We find that the twist of the boundary curve (which is also the ``spin” of the diamond) is quantized in integer or half-integer multiples of the ratio of the Planck length to the diamond edge length.

HEP - theorymathematical physics

Audience: researchers in the topic

Physics @ Boundaries Workshop