Strong force and beta function

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Euler's Beta and Gamma functions are related to string theory amplitudes, specifically the Veneziano amplitude for open strings and the Virasoro-Shapiro amplitude for closed strings, which model high-energy hadron scattering. The strong force is measured through the coupling constant, which is described by the beta function in the context of renormalization group theory. The beta function indicates how this coupling constant changes with the momentum-renormalization scale. While the beta function and Euler's functions are connected through dimensional regularization, they serve different purposes in quantum field theory. Understanding these concepts is crucial for grasping the complexities of the strong force in particle physics.
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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
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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