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| Coleman and Weinberg | |
|---|---|
| Name | Coleman and Weinberg |
| Fields | Quantum field theory, Particle physics, Quantum electrodynamics |
| Notable works | Radiative mechanism (1960) |
| Associated institutions | Harvard University, Princeton University, Cornell University |
Coleman and Weinberg.
Coleman and Weinberg refer to the 1973 theoretical result by Sidney Coleman and Erick Weinberg that demonstrated how radiative corrections in quantum field theory can induce spontaneous symmetry breaking in models lacking an explicit negative-mass-squared term, linking ideas from Julian Schwinger and Richard Feynman to later developments in electroweak theory and grand unified theory. The result influenced research at institutions such as Harvard University and Princeton University, informed model-building in Supersymmetry and Technicolor, and intersected with experimental programs at laboratories like CERN and Fermilab.
The Coleman–Weinberg result arises in perturbative quantum field theory and illustrates how loop effects associated with fields such as scalar fields, gauge bosons, and fermions modify the classical scalar potential. Key figures connected to its dissemination include Kenneth Wilson for renormalization-group ideas, Steven Weinberg (note the different Weinberg), and contemporaries like Gerard 't Hooft and Martinus Veltman who formalized renormalized perturbation theory. The mechanism provides a theoretical route from scale-invariant classical lagrangians toward dynamically generated mass scales, thereby connecting to the Hierarchy problem and to approaches explored in GUT proposals by groups including Georgi–Glashow.
The conceptual roots trace to the development of renormalization by Sin-Itiro Tomonaga, Julian Schwinger, and Richard Feynman and to symmetry-breaking paradigms exemplified in works by Yoichiro Nambu and Jeffrey Goldstone. Interest in radiative symmetry breaking grew amidst the construction of the Standard Model by Sheldon Glashow, Steven Weinberg and Abdus Salam, and in later attempts to address mass generation beyond the Higgs mechanism considered at University of Cambridge and CERN. Theoretical tools used include the renormalization group introduced by Kenneth Wilson, effective potential techniques advanced by Jackiw and Coleman himself, and loop computations formalized by t'Hooft–Veltman methods.
Coleman and Weinberg showed that a classically scale-invariant scalar theory coupled to gauge fields acquires a nontrivial vacuum through one-loop radiative corrections, producing spontaneous symmetry breaking without an explicit tachyonic mass term. Their construction used models with gauge groups such as U(1) and non-Abelian analogues relevant to SU(2) and SU(3), linking to symmetry patterns encountered in Electroweak interaction and Quantum Chromodynamics. The mechanism informed model-building in frameworks including Supersymmetry, Composite Higgs models, and Technicolor, and it set the stage for radiative-breaking scenarios in Grand Unification proposals like SU(5) and SO(10).
The formal derivation employs the one-loop effective potential V_eff(phi) computed via functional determinants for scalar, fermion, and gauge fluctuations around a background field phi, using regularization schemes such as dimensional regularization pioneered by Gerard 't Hooft and Martinus Veltman and renormalization conventions akin to those introduced by Bogoliubov and Hepp. V_eff contains logarithmic terms proportional to beta functions derived from renormalization-group equations developed by Callan and Symanzik, with extrema of V_eff determined by balancing classical quartic couplings against loop-induced logs. The minimization condition yields a scale via dimensional transmutation analogous to the mechanism in Quantum Chromodynamics that produces Lambda_QCD.
Physically, radiative symmetry breaking implies that mass scales such as scalar masses, gauge boson masses, and fermion masses can originate from quantum corrections tied to running couplings, influencing scenarios for the Higgs boson mass and for electroweak symmetry breaking explored at LEP and later at LHC. The mechanism motivated radiative electroweak symmetry breaking in MSSM constructions studied at Fermilab and CERN and was adapted in proposals for conformal extensions investigated by groups at Perimeter Institute and SLAC National Accelerator Laboratory. It also intersects with cosmological model building considered by Alan Guth and Andrei Linde in inflationary model analyses.
Experimental implications focus on scalar sector properties accessible at facilities such as LHC, LEP, and Tevatron, including precise measurements of scalar self-couplings, gauge boson couplings, and searches for additional scalar resonances predicted by radiative-breaking models. Phenomenological studies employed tools developed by collaborations at ATLAS and CMS to constrain parameter spaces, while precision electroweak fits by groups using data from SLAC and LEP Electroweak Working Group probed loop-sensitive observables tied to the mechanism. Neutrino experiments at Super-Kamiokande and IceCube and flavor programs at Belle and BaBar indirectly constrain some model variants through loop-induced processes.
Critiques of the Coleman–Weinberg approach emphasize fine-tuning challenges connected to the Hierarchy problem and sensitivity to higher-loop corrections highlighted by Steven Weinberg and by later analyses from John Ellis and collaborators. Extensions involve embedding radiative breaking in Supersymmetry, invoking conformal symmetry in AdS/CFT-inspired constructions by Juan Maldacena, or coupling to hidden sectors studied in dark-sector programs at CERN and SLAC. Nonperturbative investigations leveraging lattice techniques from groups at CERN and Fermilab aim to assess the robustness of loop-induced minima, while modern effective field theory approaches by Howard Georgi recast the mechanism within operator expansions.