Imaginary Time in Spin Foams: How is it Utilized in Quantum Gravity Theories?

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SUMMARY

Imaginary time plays a crucial role in Quantum Mechanics (QM) and Quantum Field Theory (QFT) by facilitating the convergence of oscillatory path integrals and addressing non-semibounded terms in Minkowski spacetime. In Causal Dynamical Triangulation (CDT), imaginary time is similarly employed after restricting the path integral to causal configurations. The discussion raises questions about the treatment of oscillatory terms in spin foams, particularly referencing Perez's notes where Equation 27 indicates the presence of the imaginary unit in the path integral, suggesting that Euclidean spin foams yield geometries with Euclidean signatures through specific imaginary time substitutions.

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  • Knowledge of Causal Dynamical Triangulation (CDT) methodology
  • Basic grasp of spin foam models in quantum gravity
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  • Review Perez's notes on spin foams, particularly Equation 27 and its significance
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In QM and QFT, imaginary time is used to make the oscillatory path integral converge, and also to handle terms that are not semibounded in Minkowski spacetime.

In CDT, imaginary time is also used after the path integral is restricted to "causal" configurations.

How is the oscillatory term handled in spin foams?
 
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Is this not the point of Euclidean spin-foams?
 
genneth said:
Is this not the point of Euclidean spin-foams?

Looking in Perez's notes, Eq 27 for a Euclidean spin foam, it looks like he still has the i in the path integral. I guess the Euclidean means that it produces a geometry with Euclidean signature (I guess he takes only one of the two imaginary time replacements)?
 

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