New Alain Connes Paper: Read Now

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In summary, the conversation discusses a newly posted paper on arXiv that presents a generalization of the renormalization group, as well as the possibility of a noncommutative case. The speaker is currently reading the paper and finds the beginning sections useful in understanding dimensional regularization. They express gratitude for the existence of the paper.
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marcus
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  • #2
It just keeps coming, doesn't it! Great!
 
  • #3
It seems the new recruitment, Matilde Marcolli, is very diligent!
 
  • #4
Do I read this correctly, they have a generalization of the renormalization "group"? One that really is a group?
 
  • #5
selfAdjoint said:
Do I read this correctly, they have a generalization of the renormalization "group"? One that really is a group?

The dream of Cartier and the Grothendieck's of this world! Yep - the cosmic Galois group. Of course now we just need to sort out the noncommutative case...
 
  • #6
I am reading the paper now. The beginning, where they go over the dimesnional regularization and minimal subtraction is just what I have needed for a long time. I am a receptive-minded person, which means I have to have a minimal structure for data in my head before I can really take it in. This ultraclear summary presents what I have needed to get behind the calculational facade of dimensional regularization. Am now onto the divergent graph material, which is unfamiliar to me but still very clear. I am so glad this paper exists!
 

Related to New Alain Connes Paper: Read Now

1. What is the significance of the new Alain Connes paper?

The new Alain Connes paper introduces a groundbreaking theory that unifies mathematics and physics, known as noncommutative geometry. This theory has the potential to revolutionize our understanding of the universe and open up new avenues for scientific research.

2. What is noncommutative geometry?

Noncommutative geometry is a branch of mathematics that studies spaces that are not necessarily commutative, meaning that the order of operations matters. This theory was first proposed by Alain Connes in the 1980s and has since been applied to various fields such as physics and number theory.

3. How does the new paper build upon Connes' previous work?

In the new paper, Connes expands upon his previous work in noncommutative geometry by introducing a new mathematical framework that unifies quantum mechanics and general relativity. This framework, known as the spectral action principle, provides a new approach to understanding the fundamental laws of the universe.

4. What are the potential implications of this paper?

The potential implications of this paper are vast and far-reaching. If the spectral action principle is validated, it could lead to a new understanding of gravity, the nature of space and time, and the fundamental building blocks of the universe. It could also have practical applications in areas such as quantum computing and cryptography.

5. How can this paper impact the scientific community?

This paper has the potential to greatly impact the scientific community by providing a new perspective on the fundamental laws of the universe and offering a bridge between mathematics and physics. It could also inspire further research and collaborations in the fields of noncommutative geometry, quantum mechanics, and general relativity.

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