Quantization of Causal Diamonds in 2+1 Dimensional Gravity

Explore a detailed physics seminar presentation that delves into the reduced phase space quantization of causal diamonds in 2+1 dimensional gravity with nonpositive cosmological constant. Learn how the system is defined through the domain of dependence of a spacelike topological disk with fixed boundary metrics, and discover the process of solving constraints in constant-mean-curvature time gauge while removing spatial gauge redundancy. Understand how the phase space relates to the cotangent bundle of orientation-preserving diffeomorphisms of the circle modulo the projective special linear subgroup. Examine the classical states corresponding to causal diamonds embedded in AdS3 or Mink3, and follow the application of Isham's group-theoretic quantization scheme due to the phase space's lack of global coordinate system. Investigate how the resulting Hilbert space carries an irreducible unitary representation of the BMS3 group and can be realized through wavefunctions on a coadjoint orbit of Virasoro. Discover the surprising quantization of the diamond boundary loop twist in terms of the ratio between Planck length and corner length.