Four based SO+(1,2) holonomies reconstruct a unique strictly convex tetrahedron in dS^3 or AdS^3, with det G selecting the model and recovering Euclidean cases via SU(2).
Polyhedra in loop quantum gravity
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abstract
Interwiners are the building blocks of spin-network states. The space of intertwiners is the quantization of a classical symplectic manifold introduced by Kapovich and Millson. Here we show that a theorem by Minkowski allows us to interpret generic configurations in this space as bounded convex polyhedra in Euclidean space: a polyhedron is uniquely described by the areas and normals to its faces. We provide a reconstruction of the geometry of the polyhedron: we give formulas for the edge lengths, the volume and the adjacency of its faces. At the quantum level, this correspondence allows us to identify an intertwiner with the state of a quantum polyhedron, thus generalizing the notion of quantum tetrahedron familiar in the loop quantum gravity literature. Moreover, coherent intertwiners result to be peaked on the classical geometry of polyhedra. We discuss the relevance of this result for loop quantum gravity. In particular, coherent spin-network states with nodes of arbitrary valence represent a collection of semiclassical polyhedra. Furthermore, we introduce an operator that measures the volume of a quantum polyhedron and examine its relation with the standard volume operator of loop quantum gravity. We also comment on the semiclassical limit of spinfoams with non-simplicial graphs.
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Typical entanglement entropy with fixed global charge is given by the local thermal entropy at fixed charge density for both U(1) and SU(2) symmetries in the thermodynamic limit.
Using two large reference spins in rotational group averaging recovers the standard quantum spin state description in the large limit.
EHT observations of Sgr A* constrain deviations from GR black hole solutions including regular BHs, string-inspired spacetimes, and BH mimickers, with some limits exceeding cosmological bounds.
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Generalized Minkowski Theorem for Tetrahedra in ${\rm dS}^3$ and ${\rm AdS}^3$
Four based SO+(1,2) holonomies reconstruct a unique strictly convex tetrahedron in dS^3 or AdS^3, with det G selecting the model and recovering Euclidean cases via SU(2).
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Typical entanglement entropy with charge conservation
Typical entanglement entropy with fixed global charge is given by the local thermal entropy at fixed charge density for both U(1) and SU(2) symmetries in the thermodynamic limit.
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Complete Relational Description of Spin in a Quantum Background
Using two large reference spins in rotational group averaging recovers the standard quantum spin state description in the large limit.
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Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A$^*$
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