Strong force and beta function

In summary, the conversation discusses the relationship between Euler's beta/gamma function identities and the strong force. The beta function is a renormalization-group quantity used to describe the change of the coupling constant with the momentum-renormalization scale. It has no direct connection to Euler's functions, but they arise in dimensional regularization, a common method in quantum field theory. The conversation also mentions the Veneziano and Virasoro-Shapiro amplitudes, which use Euler's functions to model high-energy hadron scattering in string theory.
  • #1
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I heard that one of Euler's Beta/Gamma function identities models the strong force. I was just wondering how it did this. (This might be a stupid question) How do we measure the strong force, and how is it a function of two variables?
 
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  • #2
The ##\beta## function is a renormalization-group quantity describing how the coupling constant "runs" with the change of the momentum-renormalization scale. It has nothing to do with Euler's beta and gamma function, except that these occur in a natural way when using dimensional regularization, which is common practice in perturbative QCD and all modern practitioners of relativistic QFT because it's a very convenient regularization scheme for gauge theories.
 
  • #3
I suspect the OP is referring to the Veneziano amplitude of open-string theory and the Virasoro-Shapiro amplitude of closed-string theory, which model high-energy hadron scattering, and which involve the Euler beta and gamma functions: http://en.wikipedia.org/wiki/Veneziano_amplitude
 

FAQ: Strong force and beta function

1. What is the strong force?

The strong force is one of the four fundamental forces of nature, along with gravity, electromagnetism, and weak force. It is responsible for holding together the nucleus of an atom by overcoming the repulsive force between positively charged protons.

2. How is the strong force related to the beta function?

The beta function is a mathematical tool used in quantum field theory to study the behavior of the strong force. It helps us understand how the strong force changes as we move to different energy scales.

3. What is the role of the strong force in nuclear reactions?

The strong force plays a crucial role in nuclear reactions by binding together the protons and neutrons in the nucleus. It is responsible for the stability and structure of the nucleus, and without it, atoms would not exist.

4. How does the strong force differ from the other fundamental forces?

The strong force is different from the other fundamental forces in several ways. It is the strongest force, but it only acts over a very short distance, unlike gravity and electromagnetism, which have infinite range. It also has a different mathematical description compared to the other forces.

5. Can the strong force be unified with the other fundamental forces?

Currently, scientists are working on developing a theory that unifies all four fundamental forces, including the strong force. This theory, known as the theory of everything, is still a work in progress and has not been fully realized yet.

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