{"query": "Yang-Mills existence and the mass gap", "count": 20, "results": [{"id": "card_question_yang_mills", "title": "Yang-Mills existence and the mass gap", "shelf": "millennium", "surface": "secular", "snippet": "Yang-Mills existence and the mass gap. A quantum Yang-Mills theory exists on four-dimensional Euclidean space for every compact simple gauge group, and has a mass gap greater than zero. Its chart is t", "authority_tier": "reference", "source": "Clay Mathematics Institute, the Millennium Prize Problems (2000)", "readable": false, "generated": false}, {"id": "card_spine_millennium_sources", "title": "The Millennium sources — the papers behind the seven sticks", "shelf": "spine", "surface": "secular", "snippet": "63 sources located for the seven Millennium sticks (Riemann, Birch and Swinnerton-Dyer, Navier-Stokes, Yang-Mills, P versus NP, Hodge, Poincare), one reference card each: the bibliographic record, DOI", "authority_tier": "reference", "source": "The Millennium sources — a spine of located records", "readable": false, "generated": false}, {"id": "card_joint_renormalization_group", "title": "The renormalization group, and the continuum limit as the question", "shelf": "codex", "surface": "secular", "snippet": "Wilson's lattice (1974) and Forster, Nelson and Stephen's randomly stirred fluid (1977) run the same renormalization group: a coupling that changes with scale, a finite system whose continuum limit is", "authority_tier": "engine_derived", "source": "Narrow Highway - the Millennium floor, a joint found in the literature (operator seed)", "readable": false, "generated": false}, {"id": "card_src_mill_forster_nelson_stephen_1977", "title": "D. Forster 1977 — Large-distance and long-time properties of a randomly stirred fluid", "shelf": "millennium", "surface": "secular", "snippet": "D. Forster, D. R. Nelson, M. J. Stephen (1977). Large-distance and long-time properties of a randomly stirred fluid. Phys. Rev. A 16 (1977) 732–749. DOI 10.1103/PhysRevA.16.732. Canonical: https://doi", "authority_tier": "reference", "source": "D. Forster, D. R. Nelson, M. J. Stephen (1977), Phys. Rev. A 16 (1977) 732–749", "readable": false, "generated": false}, {"id": "card_builder_chen_ning_yang", "title": "Chen Ning Yang", "shelf": "builders", "surface": "secular", "snippet": "Chen Ning Yang (1922-2024 AD) - physics. non-abelian gauge theory with Mills (1954), and with Lee the prediction of parity violation (1956) - the trunk of the Standard Model (A builder of the Floor of", "authority_tier": "reference", "source": "The builders of the Floor - credited with love, calibrated to the plumb-line", "readable": false, "generated": false}, {"id": "card_src_mill_odlyzko_1987", "title": "A. M. Odlyzko 1987 — On the distribution of spacings between zeros of the zeta function", "shelf": "millennium", "surface": "secular", "snippet": "A. M. Odlyzko (1987). On the distribution of spacings between zeros of the zeta function. Math. Comp. 48 (1987) 273–308. DOI 10.1090/S0025-5718-1987-0866115-0. Canonical: https://doi.org/10.1090/S0025", "authority_tier": "reference", "source": "A. M. Odlyzko (1987), Math. Comp. 48 (1987) 273–308", "readable": false, "generated": false}, {"id": "card_chart_ym_measure", "title": "The Yang-Mills mass gap, as a measure", "shelf": "codex", "surface": "secular", "snippet": "The Yang-Mills mass gap, as a measure. A chart on the one map: this is the tick stick stick_yang_mills_the_mass_gap_is_a_measure, placed at the node it charts. Basis: the stick reads the gap as Delta ", "authority_tier": "engine_derived", "source": "Narrow Highway - a chart: a tick stick placed on the one map", "readable": false, "generated": false}, {"id": "card_src_mill_jaffe_witten_2000", "title": "A. Jaffe 2000 — Quantum Yang-Mills theory", "shelf": "millennium", "surface": "secular", "snippet": "A. Jaffe, E. Witten (2000). Quantum Yang-Mills theory. Clay Mathematics Institute, the official problem description. Canonical: https://www.claymath.org/millennium/yang-mills-the-maths-gap/. Free copy", "authority_tier": "reference", "source": "A. Jaffe, E. Witten (2000), Clay Mathematics Institute, the official problem description", "readable": false, "generated": false}, {"id": "card_src_mill_osterwalder_seiler_1978", "title": "K. Osterwalder 1978 — Gauge field theories on a lattice", "shelf": "millennium", "surface": "secular", "snippet": "K. Osterwalder, E. Seiler (1978). Gauge field theories on a lattice. Ann. Phys. 110 (1978) 440–471. DOI 10.1016/0003-4916(78)90039-8. Canonical: https://doi.org/10.1016/0003-4916(78)90039-8. No free c", "authority_tier": "reference", "source": "K. Osterwalder, E. Seiler (1978), Ann. Phys. 110 (1978) 440–471", "readable": false, "generated": false}, {"id": "card_src_mill_morningstar_peardon_1999", "title": "C. J. Morningstar 1999 — Glueball spectrum from an anisotropic lattice study", "shelf": "millennium", "surface": "secular", "snippet": "C. J. Morningstar, M. Peardon (1999). Glueball spectrum from an anisotropic lattice study. Phys. Rev. D 60 (1999) 034509. DOI 10.1103/PhysRevD.60.034509. arXiv: hep-lat/9901004. Canonical: https://doi", "authority_tier": "reference", "source": "C. J. Morningstar, M. Peardon (1999), Phys. Rev. D 60 (1999) 034509", "readable": false, "generated": false}, {"id": "card_src_mill_wilson_1974", "title": "K. G. Wilson 1974 — Confinement of quarks", "shelf": "millennium", "surface": "secular", "snippet": "K. G. Wilson (1974). Confinement of quarks. Phys. Rev. D 10 (1974) 2445–2459. DOI 10.1103/PhysRevD.10.2445. Canonical: https://doi.org/10.1103/PhysRevD.10.2445. No free copy found; cited by its record", "authority_tier": "reference", "source": "K. G. Wilson (1974), Phys. Rev. D 10 (1974) 2445–2459", "readable": false, "generated": false}, {"id": "card_src_mill_politzer_1973", "title": "H. D. Politzer 1973 — Reliable perturbative results for strong interactions?", "shelf": "millennium", "surface": "secular", "snippet": "H. D. Politzer (1973). Reliable perturbative results for strong interactions?. Phys. Rev. Lett. 30 (1973) 1346–1349. DOI 10.1103/PhysRevLett.30.1346. Canonical: https://doi.org/10.1103/PhysRevLett.30.", "authority_tier": "reference", "source": "H. D. Politzer (1973), Phys. Rev. Lett. 30 (1973) 1346–1349", "readable": false, "generated": false}, {"id": "card_src_mill_flag_2021", "title": "Y. Aoki et al. (Flavour Lattice Averaging Group) 2022 — FLAG Review 2021", "shelf": "millennium", "surface": "secular", "snippet": "Y. Aoki et al. (Flavour Lattice Averaging Group) (2022). FLAG Review 2021. Eur. Phys. J. C 82 (2022) 869. DOI 10.1140/epjc/s10052-022-10536-1. arXiv: 2111.09849. Canonical: https://doi.org/10.1140/epj", "authority_tier": "reference", "source": "Y. Aoki et al. (Flavour Lattice Averaging Group) (2022), Eur. Phys. J. C 82 (2022) 869", "readable": false, "generated": false}, {"id": "card_src_mill_gross_wilczek_1973", "title": "D. J. Gross 1973 — Ultraviolet behavior of non-abelian gauge theories", "shelf": "millennium", "surface": "secular", "snippet": "D. J. Gross, F. Wilczek (1973). Ultraviolet behavior of non-abelian gauge theories. Phys. Rev. Lett. 30 (1973) 1343–1346. DOI 10.1103/PhysRevLett.30.1343. Canonical: https://doi.org/10.1103/PhysRevLet", "authority_tier": "reference", "source": "D. J. Gross, F. Wilczek (1973), Phys. Rev. Lett. 30 (1973) 1343–1346", "readable": false, "generated": false}, {"id": "card_src_mill_drouffe_zuber_1983", "title": "J.-M. Drouffe 1983 — Strong coupling and mean field methods in lattice gauge theories", "shelf": "millennium", "surface": "secular", "snippet": "J.-M. Drouffe, J.-B. Zuber (1983). Strong coupling and mean field methods in lattice gauge theories. Phys. Rep. 102 (1983) 1–119. DOI 10.1016/0370-1573(83)90034-0. Canonical: https://doi.org/10.1016/0", "authority_tier": "reference", "source": "J.-M. Drouffe, J.-B. Zuber (1983), Phys. Rep. 102 (1983) 1–119", "readable": false, "generated": false}, {"id": "card_floor_yang_mills", "title": "The Yang-Mills chain - from the gauge field and the axioms to the mass gap", "shelf": "codex", "surface": "secular", "snippet": "Two trees. The gauge field: Maxwell, Weyl's gauge principle (1929), Yang and Mills' non-abelian field (1954). The axioms: Wightman's (1956) and Osterwalder-Schrader's Euclidean ones (1973) - what it m", "authority_tier": "engine_derived", "source": "Narrow Highway - a chain on the one map (operator seed)", "readable": false, "generated": false}, {"id": "card_src_etym_craze_mill_crazing_mill", "title": "craze-mill; crazing-mill", "shelf": "etymology", "surface": "secular", "snippet": "craze-mill; crazing-mill: etymology (Webster 1913) — n.: [See 1st Craze.]. From Webster's Revised Unabridged Dictionary (1913), public domain.", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_chain_yang_mills_1954", "title": "Yang 1954 — Conservation of isotopic spin and isotopic gauge invariance", "shelf": "codex", "surface": "secular", "snippet": "C. N. Yang, R. L. Mills (1954). Conservation of isotopic spin and isotopic gauge invariance. Phys. Rev. 96 (1954) 191–195. DOI 10.1103/PhysRev.96.191. Canonical: https://doi.org/10.1103/PhysRev.96.191", "authority_tier": "reference", "source": "C. N. Yang, R. L. Mills (1954), Phys. Rev. 96 (1954) 191–195", "readable": false, "generated": false}, {"id": "card_src_lex_g6061", "title": "G6061 — μύλινος (mulinos): mill", "shelf": "lexicon", "surface": "secular", "snippet": "μύλινος (mulinos), Strong's G6061: mill. μύλινος , -η, -ον (μύλος), __1. made of mill-stone (C.l. 3371) __2. = μυλικός : Rev.18:21 (μύλον, T).† (AS)", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "readable": false, "generated": false}, {"id": "card_src_etym_walk_mill", "title": "walk-mill", "shelf": "etymology", "surface": "secular", "snippet": "walk-mill: etymology (Webster 1913) — n.: [Walk to Walking Leaf, or full + mill.]. From Webster's Revised Unabridged Dictionary (1913), public domain.", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_question_yang_mills"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}