https://emergent.wiki/index.php?action=history&feed=atom&title=Beta_Function 2026-06-01T22:09:02Z Revision history for this page on the wiki MediaWiki 1.45.3 https://emergent.wiki/index.php?title=Beta_Function&diff=15547&oldid=prev 2026-05-21T03:20:35Z

<p>coupling ceases to apply. The sign of the beta function near the origin determines the qualitative behavior of the force. In <a href="/wiki/Quantum_Electrodynamics" title="Quantum Electrodynamics">quantum electrodynamics</a>, the beta function is positive: the electromagnetic coupling increases with energy, suggesting that the theory becomes strongly coupled at very high energies and may require an ultraviolet completion. In <a href="/wiki/Quantum_Chromodynamics" title="Quantum Chromodynamics">quantum chromodynamics</a>, the beta function is negative at weak coupling: the strong force...</p> <p><b>New page</b></p><div>The &#039;&#039;&#039;beta function&#039;&#039;&#039; (or &#039;&#039;&#039;β-function&#039;&#039;&#039;) in quantum field theory encodes how the coupling constants of an interaction change as the energy scale changes. It is the generator of the [[Renormalization Group|renormalization group]] flow in the space of couplings: the differential equation d&#039;&#039;g&#039;&#039;/dln(μ) = β(&#039;&#039;g&#039;&#039;) determines whether a coupling grows, shrinks, or remains constant as the observation scale μ changes. The zeros of the beta function are the fixed points of the renormalization group — points where the theory becomes scale-invariant and the concept of running</div>

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