从爱因斯坦到引力量子场论:引力规范理论百年历程与范式转换FROM EINSTEIN TO GRAVITATIONAL QUANTUM FIELD THEORY: A CENTURY OF GRAVITY GAUGE THEORY AND ITS PARADIGM SHIFT
高远坤,吴岳良
摘要(Abstract):
引力与规范原理的融合,自广义相对论诞生以来,一直是理论物理百年探索的核心主线。本文以从“几何范式”到“物质范式”的视角转换为纲领,系统梳理了这一融合进程的两大阶段。第一阶段以规范原理为起点,经由Utiyama的局域洛伦兹规范理论、Sciama的自旋-挠率耦合、Kibble的庞加莱规范引力,直至Hehl等建立的黎曼-嘉当时空几何与规范场论框架,深刻揭示了规范原理与时空引力的内在联系。然而,该阶段始终沿循“从时空几何出发”的传统范式。第二阶段以本文作者之一提出的引力量子场论为标志,实现了根本性的范式转换:将基本粒子自旋所对应的规范对称性SP(1,3)确立为物质基本组元独立且第一性的内禀对称性。由此涌现出双标架时空、非对易的纤维丛式引力规范时空等全新结构,使引力动力学从量子场论基本原理中自然导出,突破了传统弯曲时空几何的框架限制。本文系统阐述了两大阶段的历史脉络、核心物理思想、关键数学结构及场方程特征,对比分析了其本质差异与内在联系,并阐明了在引力量子场论框架下构建广义标准模型、实现四种基本相互作用统一描述的理论自洽性。
关键词(KeyWords): 引力规范理论;引力量子场论
基金项目(Foundation): 国家重点研发计划(批准号:2020YFC2201501);; 国家自然科学基金(批准号:12547104,12441504,12147103,11821505);; 中国科学院战略性先导项目资助的课题
作者(Author): 高远坤,吴岳良
DOI: 10.27024/j.wlygc.2026.05.15.is
参考文献(References):
- [1] ROVELLI C.Quantum gravity[M].Cambridge:Cambridge University Press,2004.
- [2] EINSTEIN A.Approximative Integration of the Field Equations of Gravitation[J].Sitzungsberichte der Preu??ischen Akademie der Wissenschaften zu Berlin (Mathematisch-Physikalische Klasse),1916,1916:688-696.
- [3] ESPOSITO G.An Introduction to quantum gravity[J].arXiv preprint arXiv:1108.3269,2011.
- [4] ROVELLI C.Notes for a brief history of quantum gravity[C]//9th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity,Gravitation and Relativistic Field Theories (MG 9).2000:742-768.
- [5] ROSENFELD L.??ber die Gravitationswirkungen des Lichtes[J].Zeitschrift für Physik,1930,65(9):589-599.
- [6] ROSENFELD L.Zur Quantelung der Wellenfelder[J].Annalen der Physik,1930,397(1):113-152.
- [7] FIERZ M.??ber die relativistische Theorie kr??ftefreier Teilchen mit beliebigem Spin[J].Helvetica Physica Acta,1939,12(I):3.
- [8] BLOKHINTSEV D,GAL'PERIN F.Neutrino hypothesis and conservation of energy[J].Pod Znamenem Marxisma,1934,6:147-157.
- [9] GUPTA S N.Quantization of Einstein's gravitational field:general treatment[J].Proceedings of the Physical Society A,1952,65:608-619.
- [10] FEYNMAN R P.Quantum theory of gravitation[J].Acta Physica Polonica,1963,24:697-722.
- [11] DEWITT B S.The quantization of geometry[C]//International Conference on Relativistic Theories of Gravitation.1964:131-147.
- [12] DESER S,VAN NIEUWENHUIZEN P.Nonrenormalizability of the Quantized Dirac-Einstein System[J].Physical Review D,1974,10:411.
- [13] DESER S,VAN NIEUWENHUIZEN P.One Loop Divergences of Quantized Einstein-Maxwell Fields[J].Physical Review D,1974,10:401.
- [14] 'T HOOFT G,VELTMAN M J G.One-loop divergencies in the theory of gravitation[J].Annales de l'Institut Henri Poincaré A,Physique théorique,1974,20(1):69-94.
- [15] 'T HOOFT G.An algorithm for the poles at dimension four in the dimensional regularization procedure[J].Nuclear Physics B,1973,62:444-460.
- [16] STELLE K S.Renormalization of Higher Derivative Quantum Gravity[J].Physical Review D,1977,16:953-969.
- [17] FREEDMAN D Z,VAN NIEUWENHUIZEN P,FERRARA S.Progress Toward a Theory of Supergravity[J].Physical Review D,1976,13:3214-3218.
- [18] BERGMANN P G.Non-Linear Field Theories[J].Physical Review,1949,75:680-685.
- [19] DIRAC P A M.The Hamiltonian form of field dynamics[J].Canadian Journal of Mathematics,1951,3:1-23.
- [20] ARNOWITT R L,DESER S,MISNER C W.The Dynamics of general relativity[J].General Relativity and Gravitation,2008,40:1997-2027.
- [21] PERES A.On Cauchy's problem in general relativity-II[J].Il Nuovo Cimento (1955—1965),1962,26(1):53-62.
- [22] WHEELER J A.Geometrodynamics and the issue of final state[C]//Les Houches Summer Shcool of Theoretical Physics:Relativity,Groups and Topology,1964:317-522.
- [23] DEWITT B S.Quantum Theory of Gravity.1.The Canonical Theory[J].Physical Review,1967,160:1113-1148.
- [24] PENROSE R.Twistor theory and the Einstein vacuum[J].Classical and Quantum Gravity,1999,16:A113-A130.
- [25] PENROSE R,MACCALLUM M A H.Twistor theory:An Approach to the quantization of fields and space-time[J].Physics Reports,1972,6:241-316.
- [26] CONNES A,MARCOLLI M.Noncommutative Geometry,Quantum Fields and Motives[M].Providence,R.I.:American Mathematical Society,2019.
- [27] CONNES A.Noncommutative geometry[M].San Diego:Academic Press,1994.
- [28] HAWKING S W.Quantum Gravity and Path Integrals[J].Physical Review D,1978,18:1747-1753.
- [29] GIBBONS G W,HAWKING S W.Action Integrals and Partition Functions in Quantum Gravity[J].Physical Review D,1977,15:2752-2756.
- [30] WEYL H.Raum,zeit,materie:Volume 7[M].Berlin:Springer,1918.
- [31] WEYL H.Gravitation und Elektrizit??t[J].Sitzungsberichte der K??niglich Preussischen Akademie der Wissenschaften,1918:465-478.
- [32] JACKSON J D,OKUN L B.Historical roots of gauge invariance[J].Review of Modern Physics,2001,73:663-680.
- [33] WEYL H.Gravitation and the electron[J].Proceedings of the National Academy of Sciences,1929,15(4):323-334.
- [34] LONDON F.Die Theorie von Weyl und die Quantenmechanik[J].Naturwissenschaften,1927,15(8):187-187.
- [35] YANG C N,MILLS R L.Conservation of Isotopic Spin and Isotopic Gauge Invariance[J].Physical Review,1954,96:191-195.
- [36] SALAMA.Proceedings of the 8th Nobel Symposium[C].Stockholm:Almqvist & Wicksell,1968.
- [37] WEINBERG S.A Model of Leptons[J].Physical Review Letters,1967,19:1264-1266.
- [38] GLASHOW S L.Partial Symmetries of Weak Interactions[J].Nuclear Physics,1961,22:579-588.
- [39] POLITZER H D.Reliable Perturbative Results for Strong Interactions?[J].Physical Review Letters,1973,30:1346-1349.
- [40] GROSS D J,WILCZEK F.Ultraviolet Behavior of Nonabelian Gauge Theories[J].Physical Review Letters,1973,30:1343-1346.
- [41] FRITZSCH H,GELL-MANN M,LEUTWYLER H.Advantages of the Color Octet Gluon Picture[J].Physical Letters B,1973,47:365-368.
- [42] SCHWARTZ M D.Quantum Field Theory and the Standard Model[M].Cambridge:Cambridge University Press,2014.
- [43] EDDINGTON A S.A generalisation of Weyl's theory of the electromagnetic and gravitational fields[J].Proceedings of the Royal Society of London.Series A,Containing Papers of a Mathematical and Physical Character,1921,99(697):104-122.
- [44] CARTAN ??.La géométrie des espaces de Riemann[M].Paris:Gauthier-Villars,1925.
- [45] CARTAN ??.Sur les variétés à connexion affine et la théorie de la relativité généralisée (première partie)[C]//Annales scientifiques de l'??cole normale supérieure:Volume 40.1923:325-412.
- [46] CARTAN ??.Sur une généralisation de la notion de courbure de Riemann et les espaces à torsion[J].Comptes Rendus de l'Académie des Sciences.Paris,1922,174:593-595.
- [47] WEYL H.Elektron und Gravitation.I[J].Zeitschrift für Physik,1929,56(5):330-352.
- [48] UTIYAMA R.Invariant theoretical interpretation of interaction[J].Physical Review,1956,101:1597-1607.
- [49] SCIAMA D W.On the analogy between charge and spin in general relativity[J].Recent developments in general relativity,1962:415.
- [50] ROSENFELD L J H C.Sur le tenseur d'impulsion-énergie[M].Bruxelles:Palais des académies,1940.
- [51] BELINFANTE F J.On the current and the density of the electric charge,the energy,the linear momentum and the angular momentum of arbitrary fields[J].Physica,1940,7(5):449-474.
- [52] KIBBLE T W B.Lorentz invariance and the gravitational field[J].Journal of Mathematical Physics,1961,2:212-221.
- [53] HEHL F W,VON DER HEYDE P,KERLICK G D,et al.General Relativity with Spin and Torsion:Foundations and Prospects[J].Review of Modern Physics,1976,48:393-416.
- [54] IVANENKO D,SARDANASHVILY G.The Gauge Treatment of Gravity[J].Physics Reports,1983,94:1-45.
- [55] HEHL F W,MCCREA J D,MIELKE E W,et al.Metric affine gauge theory of gravity:Field equations,Noether identities,world spinors,and breaking of dilation invariance[J].Physics Reports,1995,258:1-171.
- [56] HEISENBERG L.Review on f(Q) gravity[J].Physics Reports,2024,1066:1-78.
- [57] OBUKHOV Y N.Poincaré Gauge Gravity Primer[J].Lecture Notes in Physics,2023,1017:105-143.
- [58] PONOMAREV V N,BARVINSKIJ A O,OBUKHOV Y N.Gauge approach and quantization methods in gravity theory:Volume 10[M].Nauka Moscow,2017.
- [59] WU Y L.Gravitization equation and zero energy momentum tensor theorem with cancellation law in gravitational quantum field theory[J].Physical Letters B,2025,868:139689.
- [60] WU Y L.Foundations of the Hyperunified Field Theory[M].World Scientific,2022.
- [61] WU Y L.Gravidynamics,spinodynamics and electrodynamics within the framework of gravitational quantum field theory[J].Science China Physics,Mechanics & Astronomy,2023,66(6):260411.
- [62] WU Y L.The foundation of the hyperunified field theory Ⅱ—Fundamental interaction and evolving universe[J].International Journal of Modern Physics A,2021,36(28):2143002.
- [63] WU Y L.The foundation of the hyperunified field theory Ⅰ—Fundamental building block and symmetry[J].International Journal of Modern Physics A,2021,36(28):2143001.
- [64] WU Y L.Hyperunified field theory and gravitational gauge-geometry duality[J].The European Physical Journal C:Particles and Fields,2018,78(1):28.
- [65] WU Y L.Unified field theory of basic forces and elementary particles with gravitational origin of gauge symmetry in hyper-spacetime[J].Science Bulletin,2017,62(16):1109-1113.
- [66] WU Y L.Maximal symmetry and mass generation of Dirac fermions and gravitational gauge field theory in six-dimensional spacetime[J].Chinese Physics C,2017,41(10):103106.
- [67] WU Y L.Theory of Quantum Gravity Beyond Einstein and Space-time Dynamics with Quantum Inflation[J].International Journal of Modern Physics A,2015,30(28n29):1545002.
- [68] WU Y L.Quantum field theory of gravity with spin and scaling gauge invariance and spacetime dynamics with quantum inflation[J].Physical Review D,2016,93(2):024012.
- [69] GAO Y K,HUANG D,MA Y L,et al.Linear dynamics and classical tests of the gravitational quantum field theory[J].Physical Review D,2024,109(6):064072.
- [70] GAO Y K,HUANG D,WU Y L.Gravitational wave generation and detection in gravitational quantum field theory[J].The European Physical Journal C,2025,85(10):1159.
- [71] XU C,JIN H B,WU Y L.Detector response to gravitational wave polarizations ingravitational quantum field theory[EB/OL].(2025-04-02)[2026-05-18].https://arxiv.org/abs/2504.01809.
- [72] WU Y L.Theoretical Foundations of the General Standard Model:A Unified Framework for Particle Physics and Cosmology[J].arXiv preprint arXiv:2508.20128,2025.
- [73] WU Y L.A general theory of the standard model and the revelation of the dark side of the universe[J].Science Bulletin,2025,70:1740-1744.
- [74] XU C,JIN H B,WU Y L.Detector Response to Gravitational Wave Polarizations in Gravitational Quantum Field Theory[J].arXiv preprint arXiv:2504.01809,2025.
- [75] CHEN Y jian,XU P,WU Y liang.Post-newtonian tests of gravitational quantum field theory with spin and scaling gauge symmetry[J].The European Physical Journal C:Particles and Fields,2025,85(3):228.
- [76] GAO D,NI W T.Frame-dragging effects in a gravitational quantum field theory[J].Physical Review D,2025,111(8):084039.
- [77] WANG Q Y,TANG Y,WU Y L.Inflation in Weyl scaling invariant gravity with R3 extensions[J].Physical Review D,2023,107(8):083511.
- [78] WANG Q Y,TANG Y,WU Y L.Dark matter production in Weyl R2 inflation[J].Physical Review D,2022,106(2):023502.
- [79] CHEN G S,YANG C B,BAO S S,et al.Revisiting the fermionic quasibound states around Schwarzschild black holes with improved analytic spectrum[J].Physical Review D,2025,111(12):125006.
- [80] HUANG D,TANG Y,WU Y L.Contributions to the muon g-2 from a three-form field[J].Journal of High Energy Physics,2023,1:117.