Is Resurgence Theory and QFT the Next Quantum Mechanics Breakthrough?

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In summary: This seems like a really interesting topic. If you have any other questions, I would be happy to help you out.
  • #1
diegzumillo
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Hey there

I'm starting to work on my thesis and this is one possible subject. I'm reading a few papers (pretty much anything that appears on the first google search page) dealing with it from several different angles. From a completely general and mathematical stand to specific examples, like the Borel resummation ambiguity in the double well and how instantons relate to that.

But I haven't found anything on this forum about it. In fact, besides a few papers here and there I haven't found much at all. So I thought I'd ask here if anyone worked with this or is working right now, and has some advice to give.

BTW, I didn't know where to put this topic, here or in Quantum Mechanics.
 
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  • #2
diegzumillo said:
Hey there

I'm starting to work on my thesis and this is one possible subject. I'm reading a few papers (pretty much anything that appears on the first google search page) dealing with it from several different angles. From a completely general and mathematical stand to specific examples, like the Borel resummation ambiguity in the double well and how instantons relate to that.

But I haven't found anything on this forum about it. In fact, besides a few papers here and there I haven't found much at all. So I thought I'd ask here if anyone worked with this or is working right now, and has some advice to give.

BTW, I didn't know where to put this topic, here or in Quantum Mechanics.
Resurgence is a very interesting topic and although I am not working on it directly, it seems to me that it has been generating quite interest recently. It seems to me to be a very worthwhile topic to learn about. You are talking about a Master thesis? Of course, an important factor for you to consider is whether you have someone at your institution who can guide you in your work. You have discussed this with your adviser?
 
  • #3
PhD thesis. I did talk to an adviser. It's not his primary field but he seems interested.
 

FAQ: Is Resurgence Theory and QFT the Next Quantum Mechanics Breakthrough?

1. What is resurgence theory?

Resurgence theory is a mathematical framework used in quantum field theory (QFT) to study the behavior of non-perturbative solutions. It is based on the idea that a given physical system can have multiple perturbative expansions, each with their own domain of validity. Resurgence theory seeks to understand the connections between these different expansions and how they can be used to gain insights into the non-perturbative behavior of the system.

2. How does resurgence theory relate to QFT?

Resurgence theory is a branch of mathematics that has been applied to QFT. It provides a powerful tool for studying the non-perturbative behavior of physical systems in QFT, which is notoriously difficult to analyze using traditional perturbative methods. By connecting different perturbative expansions, resurgence theory allows for a deeper understanding of the underlying physical principles at play.

3. What are the practical applications of resurgence theory in QFT?

Resurgence theory has been applied to a wide range of problems in QFT, including the study of quantum phase transitions, confinement in gauge theories, and the behavior of black holes. It has also been used to develop new methods for calculating scattering amplitudes in QFT, which are important for particle physics experiments.

4. Can resurgence theory be tested experimentally?

Resurgence theory is a purely mathematical framework, so it cannot be tested directly in experiments. However, its applications in QFT have led to new insights and predictions that can be tested experimentally. For example, the use of resurgence theory in calculating scattering amplitudes has led to more accurate predictions for particle collisions at the Large Hadron Collider.

5. How does resurgence theory differ from other non-perturbative approaches in QFT?

Resurgence theory differs from other non-perturbative approaches, such as lattice QCD or instanton methods, in that it does not rely on specific assumptions about the underlying physics. Instead, it is a general mathematical framework that can be applied to a wide range of problems in QFT. It also has the advantage of connecting different perturbative expansions, providing a more complete picture of the non-perturbative behavior of physical systems.

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