Toller matrices T^(±) in causal spinfoam amplitudes satisfy T^(+) + T^(-) = D and admit equivalent definitions via analyticity, iε prescription, and boost-eigenvalue integrals that reproduce the Euclidean-to-Lorentzian Wick rotation.
Causal structure in spin-foams
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abstract
The metric field of general relativity is almost fully determined by its causal structure. Yet, in spin-foam models for quantum gravity, the role played by the causal structure is still largely unexplored. The goal of this paper is to clarify how causality is encoded in such models. The quest unveils the physical meaning of the orientation of the two-complex and its role as a dynamical variable. We propose a causal version of the EPRL spin-foam model and discuss the role of the causal structure in the reconstruction of a semiclassical spacetime geometry.
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In a path-integral model of timeless quantum systems, time evolution arises when a clock is prepared in a semiclassical state, showing that the cosine problem in quantum gravity follows from time-reversal invariance and neutral boundary conditions.
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Toller matrices and the Feynman $i\varepsilon$ in spinfoams
Toller matrices T^(±) in causal spinfoam amplitudes satisfy T^(+) + T^(-) = D and admit equivalent definitions via analyticity, iε prescription, and boost-eigenvalue integrals that reproduce the Euclidean-to-Lorentzian Wick rotation.
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The problem of time: a path integral view
In a path-integral model of timeless quantum systems, time evolution arises when a clock is prepared in a semiclassical state, showing that the cosine problem in quantum gravity follows from time-reversal invariance and neutral boundary conditions.