Gording, Brage; Schmidt-May, Angnis The unified standard model. (English) Zbl 1477.17037 Adv. Appl. Clifford Algebr. 30, No. 4, Paper No. 55, 27 p. (2020). Summary: The aim of this work is to find a simple mathematical framework for our established description of particle physics. We demonstrate that the particular gauge structure, group representations and charge assignments of the Standard Model particles are all captured by the algebra M \((8,\mathbb{C})\) of complex \(8 \times 8\) matrices. This algebra is well motivated by its close relation to the normed division algebra of octonions. (Anti-)particle states are identified with basis elements of the vector space M \((8, \mathbb{C})\). Gauge transformations are simply described by the algebra acting on itself. Our result shows that all particles and gauge structures of the Standard Model are contained in the tensor product of all four normed division algebras, with the quaternions providing the Lorentz representations. Interestingly, the space M \((8, \mathbb{C})\) contains two additional elements independent of the Standard Model particles, hinting at a minimal amount of new physics. Cited in 3 Documents MSC: 17A35 Nonassociative division algebras 15A66 Clifford algebras, spinors 81V22 Unified quantum theories Keywords:standard model; unification; division algebra; gauge structure PDFBibTeX XMLCite \textit{B. Gording} and \textit{A. Schmidt-May}, Adv. Appl. Clifford Algebr. 30, No. 4, Paper No. 55, 27 p. (2020; Zbl 1477.17037) Full Text: DOI arXiv References: [1] Aad, G., et al.: [ATLAS Collaboration], Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC. Phys. Lett. B 716, 1 (2012). arXiv:1207.7214 [hep-ex] [2] Abe, K. et al.: [Super-Kamiokande Collaboration], Search for proton decay via \(p \rightarrow e^+\pi^0\) and \(p \rightarrow \mu^+\pi^0\) in 0.31 megatonyears exposure of the Super-Kamiokande water Cherenkov detector. Phys. Rev. D 95(1), 012004 (2017) arXiv:1610.03597 [hep-ex] [3] Anastasiou, A.; Borsten, L.; Duff, MJ; Hughes, LJ; Nagy, S., An octonionic formulation of the M-theory algebra, JHEP, 1411, 022 (2014) · Zbl 1333.81153 [4] Babu, KS; Mohapatra, RN, Quantization of electric charge from anomaly constraints and a Majorana neutrino, Phys. Rev. D, 41, 271 (1990) [5] Baez, JC, The octonions, Bull. Am. Math. Soc., 39, 145 (2002) · Zbl 1026.17001 [6] Baez, JC; Huerta, J., Division algebras and supersymmetry I, Proc. Symp. Pure Maths., 81, 65 (2010) · Zbl 1210.81117 [7] Barducci, A.; Buccella, F.; Casalbuoni, R.; Lusanna, L.; Sorace, E., Quantized Grassmann variables and unified theories, Phys. Lett., 67B, 344 (1977) [8] Boyle, L.; Farnsworth, S., Non-commutative geometry, non-associative geometry and the standard model of particle physics, New J. Phys., 16, 12, 123027 (2014) [9] Casalbuoni, R.; Gatto, R., Unified description of quarks and leptons, Phys. Lett., 88B, 306 (1979) [10] Casalbuoni, R.; Gatto, R., Unified theories for quarks and leptons based onClifford algebras, Phys. Lett., 90B, 81 (1980) [11] Chamseddine, AH; Connes, A., The spectral action principle, Commun. Math. Phys., 186, 731-750 (1997) · Zbl 0894.58007 [12] Chamseddine, AH; Connes, A., Resilience of the spectral standard model, JHEP, 09, 104 (2012) · Zbl 1397.81412 [13] Chamseddine, AH; Connes, A.; Mukhanov, V., Geometry and the quantum: basics, JHEP, 12, 098 (2014) · Zbl 1333.81414 [14] Chatrchyan, S., et al.: [CMS Collaboration], Observation of a new Boson at a mass of 125 GeV with the CMS experiment at the LHC. Phys. Lett. B 716, 30 (2012). arXiv:1207.7235 [hep-ex] [15] Connes, A., Gravity coupled with matter and foundation of noncommutative geometry, Commun. Math. Phys., 182, 155-176 (1996) · Zbl 0881.58009 [16] de Wit, B.; Nicolai, H., The parallelizing S(7) torsion in gauged \(N=8\) upergravity, Nucl. Phys. B, 231, 506 (1984) [17] Dixon, G., Nuovo Cim. B, 105, 349 (1990) [18] Dixon, GM, Division Algebras: Octonions Complex Numbers and the Algebraic Design of Physics (1994), US: Springer, US [19] Furey, C.: Standard model physics from an algebra?. arXiv:1611.09182 [hep-th] · Zbl 1345.81059 [20] Furey, C., Unified theory of ideals, Phys. Rev. D, 86, 025024 (2012) [21] Furey, C., Generations: three prints, in colour, JHEP, 1410, 046 (2014) · Zbl 1400.81148 [22] Furey, C., Charge quantization from a number operator, Phys. Lett. B, 742, 195 (2015) · Zbl 1345.81059 [23] Furey, C., Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra, Phys. Lett. B, 785, 84 (2018) · Zbl 1398.81158 [24] Geng, CQ; Marshak, RE, Uniqueness of Quark and Lepton representations in the standard model from the anomalies viewpoint, Phys. Rev. D, 39, 693 (1989) [25] Georgi, H., The state of the ArtGauge theories, AIP Conf. Proc., 23, 575 (1975) [26] Georgi, H., An almost realistic gauge hierarchy, Phys. Lett., 108B, 283 (1982) [27] Georgi, H.; Glashow, SL, Unity of all elementary particle forces, Phys. Rev. Lett., 32, 438 (1974) [28] Georgi, H.; Quinn, HR; Weinberg, S., Hierarchy of interactions in unified gauge theories, Phys. Rev. Lett., 33, 451 (1974) [29] Gillard, AB; Gresnigt, NG, Three fermion generations with two unbroken gauge symmetries from the complex sedenions, Eur. Phys. J. C, 79, 5, 446 (2019) [30] Grinstein, B., A supersymmetric SU(5) gauge theory with no gauge hierarchy problem, Nucl. Phys. B, 206, 387 (1982) [31] Gunaydin, M., Octonionic Hilbert spaces, the Poincare Group and SU(3), J. Math. Phys., 17, 1875 (1976) [32] Gunaydin, M.; Gursey, F., Quark structure and octonions, J. Math. Phys., 14, 1651 (1973) · Zbl 0338.17004 [33] Gunaydin, M.; Gursey, F., Quark statistics and octonions, Phys. Rev. D, 9, 3387 (1974) [34] Gunaydin, M.; Warner, NP, The G2 invariant compactifications in eleven-dimensional supergravityThe G2 invariant compactifications in eleven-dimensional supergravity, Nucl. Phys. B, 248, 685 (1984) [35] Manogue, CA; Dray, T., Octonions, E(6), and particle physics, J. Phys. Conf. Ser., 254, 012005 (2010) [36] Masiero, A.; Nanopoulos, DV; Tamvakis, K.; Yanagida, T., Naturally massless Higgs doublets in supersymmetric SU(5), Phys. Lett., 115B, 380 (1982) [37] Minahan, JA; Ramond, P.; Warner, RC, A comment on anomaly cancellation in the standard model, Phys. Rev. D, 41, 715 (1990) [38] Pati, JC; Salam, A., Lepton number as the fourth color, Phys. Rev. D, 10, 275 (1974) [39] Peskin, ME; Schroeder, DV, An Introduction to Quantum Field Theory (1995), Boulder: Westview, Boulder [40] Stoica, OC, The standard model algebra—leptons, quarks, and unified theories for quarks and leptons based on Gauge from the complex Clifford algebra \(\mathbb{C}\ell_6 \), Adv. Appl. Clifford Algebras, 28, 3, 52 (2018) · Zbl 1403.81072 [41] Todorov, I.: Exceptional quantum algebra for the standard model of particle physics. arXiv:1911.13124 [hep-th] [42] Todorov, I.; Drenska, S., Octonions, exceptional Jordan algebra and the role of the group \(F_4\) in particle physics, Adv. Appl. Clifford Algebras, 28, 4, 82 (2018) · Zbl 1405.81180 [43] Weinberg, S., Recent progress in gauge theories of the weak, electromagnetic and strong interactions, J. Phys. Colloq., 34, C1, 45 (1973) [44] Weinberg, S., Recent progress in gauge theories of the weak, electromagnetic and strong interactions, Rev. Mod. Phys., 46, 255 (1974) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.