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.
Implementing causality in the spin foam quantum geometry
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abstract
We analyse the classical and quantum geometry of the Barrett-Crane spin foam model for four dimensional quantum gravity, explaining why it has to be considering as a covariant realization of the projector operator onto physical quantum gravity states. We discuss how causality requirements can be consistently implemented in this framework, and construct causal transiton amplitudes between quantum gravity states, i.e. realising in the spin foam context the Feynman propagator between states. The resulting causal spin foam model can be seen as a path integral quantization of Lorentzian first order Regge calculus, and represents a link between several approaches to quantum gravity as canonical loop quantum gravity, sum-over-histories formulations, dynamical triangulations and causal sets. In particular, we show how the resulting model can be rephrased within the framework of quantum causal sets (or histories).
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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.
Proposes a causal EPRL spin-foam model where the two-complex orientation encodes causality and aids semiclassical geometry reconstruction.
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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.
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Causal structure in spin-foams
Proposes a causal EPRL spin-foam model where the two-complex orientation encodes causality and aids semiclassical geometry reconstruction.