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

In summary, imaginary time is commonly used in QM, QFT, and CDT to handle oscillatory terms and non-semibounded terms in path integrals. In spin foams, it is also used to restrict the path integral to "causal" configurations. However, in Euclidean spin foams, only one of the two imaginary time replacements is taken, resulting in a geometry with Euclidean signature. This can be seen in Perez's notes, where the path integral still includes the term i.
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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?
 
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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)?
 

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

1. What is imaginary time in spin foams?

Imaginary time in spin foams is a concept used in theoretical physics to describe the behavior of quantum systems. It is a mathematical concept that represents the time component in a four-dimensional space-time. Unlike real time, which moves forward in a linear fashion, imaginary time moves in a direction perpendicular to real time. This allows for easier calculations in quantum systems and helps to avoid the problem of singularities that often occur when using real time.

2. How is imaginary time related to spin foams?

In the spin foam approach to quantum gravity, space-time is represented as a collection of 2-dimensional surfaces (spin networks) that evolve over imaginary time. These surfaces are made up of quanta of space-time, known as spin foams. The use of imaginary time in this approach allows for a more consistent and unified description of space-time at the quantum level.

3. What are the implications of using imaginary time in spin foams?

One of the main implications of using imaginary time in spin foams is that it allows for a more accurate description of quantum systems. This is because it avoids the problem of singularities that often occur when using real time. Additionally, the use of imaginary time in spin foams has led to new insights and predictions about the behavior of quantum systems and the nature of space-time.

4. Are there any experimental evidence for the existence of imaginary time in spin foams?

At this time, there is no direct experimental evidence for the existence of imaginary time in spin foams. However, the use of imaginary time has been successful in making predictions about the behavior of quantum systems and has been supported by various mathematical calculations. Further research and experimentation is needed to fully understand the implications of imaginary time in spin foams.

5. How does imaginary time in spin foams relate to other theories in physics?

Imaginary time in spin foams is closely related to other theories in physics, such as string theory and loop quantum gravity. In fact, the concept of imaginary time was first introduced by the physicist Stephen Hawking in his work on the thermodynamics of black holes, which is closely related to string theory. Additionally, the use of imaginary time has also been explored in other areas of physics, such as quantum mechanics and cosmology.

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