Strong force and beta function

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SUMMARY

The discussion centers on the relationship between Euler's Beta and Gamma functions and the strong force in quantum field theory. The beta function is identified as a renormalization-group quantity that describes the behavior of the coupling constant with respect to momentum-renormalization scales. It is clarified that while the beta function is related to dimensional regularization, it is distinct from Euler's functions. The conversation also references the Veneziano amplitude and Virasoro-Shapiro amplitude, which are significant in modeling high-energy hadron scattering.

PREREQUISITES
  • Understanding of quantum chromodynamics (QCD)
  • Familiarity with renormalization-group theory
  • Knowledge of dimensional regularization techniques
  • Basic concepts of string theory, particularly Veneziano and Virasoro-Shapiro amplitudes
NEXT STEPS
  • Study the beta function in quantum field theory and its implications for coupling constants
  • Explore dimensional regularization and its applications in perturbative QCD
  • Research the Veneziano amplitude and its role in high-energy particle physics
  • Investigate the Virasoro-Shapiro amplitude and its significance in string theory
USEFUL FOR

Physicists, particularly those specializing in quantum field theory, string theory researchers, and anyone interested in the mathematical modeling of fundamental forces.

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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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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.
 
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
 

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