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In particle physics, one of the grand unified theories (GUT) is based on the SO(10) Lie group. (The Lie group involved is not really the special orthogonal group SO(10), but rather its double cover Spin(10); but calling it SO(10) is the standard convention.) Before SU(5), Harald Fritzsch and Peter Minkowski and independently Howard Georgi found that all the matter contents are incorporated into a single representation, spinorial 16 of SO(10). (Historical note: the ''before'' in the previous sentence is misleading: Georgi found the SO(10) theory a few hours before finding SU(5) at the end of 1973.〔This story is told in various places; see for example, (Yukawa-Tomonaga 100th Birthday Celebration ); Fritzsch and Minkowski analyzed SO(10) in 1974.〕) ==Important subgroups== It has the branching rules to ()/Z5. : : : If the hypercharge is contained within SU(5), this is the conventional Georgi–Glashow model, with the 16 as the matter fields, the 10 as the electroweak Higgs field and the 24 within the 45 as the GUT Higgs field. The superpotential may then include renormalizable terms of the form ''Tr''(45 ⋅ 45); ''Tr''(45 ⋅ 45 ⋅ 45); 10 ⋅ 45 ⋅ 10, 10 ⋅ 16 * ⋅ 16 and 16 * ⋅ 16. The first three are responsible to the gauge symmetry breaking at low energies and give the Higgs mass, and the latter two give the matter particles masses and their Yukawa couplings to the Higgs. There is another possible branching, under which the hypercharge is a linear combination of an SU(5) generator and χ. This is known as flipped SU(5). Another important subgroup is either (× SU(2)L × SU(2)R )/Z2 or Z2 ⋊ (× SU(2)L × SU(2)R )/Z2 depending upon whether or not the left-right symmetry is broken, yielding the Pati–Salam model, whose branching rule is : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「SO(10) (physics)」の詳細全文を読む スポンサード リンク
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