Latest problem · 2026-08-16

The One-Loop Running of a Gauge Coupling

Derive the one-loop flow of g-squared in Yang-Mills theory, add matter and thresholds, then apply the same machinery to the Standard Model SU(2)_L coupling, electroweak multiplets, unification, and weakly coupled fixed points.

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Topics covered so far

Each note states a question, develops the argument, tests its assumptions, and ends with an exercise and references.

  • condensed matter18
  • mathematical physics17
  • statistical mechanics15
  • quantum information12
  • quantum field theory11
  • quantum theory11
  • particle physics2
  • classical mechanics1
  • cosmology1
  • general relativity1
  1. 08-16The One-Loop Running of a Gauge Couplingquantum field theory
  2. 08-15How Three Dimensions Learn to Behave Like Onequantum theory
  3. 08-14How Degrees of Freedom Survive Dimensional Reduction: Universal Clusters from Shielded Molecules to Species-Selective Trapscondensed matter
  4. 08-13A singular self-energy does not determine the resistivitycondensed matter
  5. 08-12A Lindblad equation does not determine trajectory entanglementquantum information
  6. 08-11Gauging trades a finite Abelian symmetry for its Fourier dualquantum field theory
  7. 08-10Interactions can dress motion without thermalizing rapiditiescondensed matter
  8. 08-09Entanglement alone does not make a quantum sensor robustquantum information
  9. 08-08Dipole conservation alone does not imply fracton order or k⁴ relaxationcondensed matter
  10. 08-07A stronger antiferromagnetic pairing vertex need not raise Tccondensed matter
  11. 08-06A complex pseudo-entropy does not establish emergent timequantum information
  12. 08-05Synthetic gauge geometry does not guarantee many-body localitycondensed matter
  13. 08-04Finite temporal bond dimension can cut off critical slowing downcondensed matter
  14. 08-03A trivial Floquet endpoint does not trivialize the drive pathcondensed matter