Matrici Gell Mana odne z predstavlen infinitezimalnih generatoriv specialnoyi unitarnoyi grupi SU 3 Voni vikoristovuyutsya v kvantovij hromodinamici i ye uzagalnennyam matric Pauli Vsogo isnuye 8 linijno nezalezhnih matric 3x3 iz odinichnim viznachnikom Yih mozhna vibrati v nastupnomu viglyadi l 1 0 1 0 1 0 0 0 0 0 displaystyle lambda 1 begin pmatrix 0 amp 1 amp 0 1 amp 0 amp 0 0 amp 0 amp 0 end pmatrix l 2 0 i 0 i 0 0 0 0 0 displaystyle lambda 2 begin pmatrix 0 amp i amp 0 i amp 0 amp 0 0 amp 0 amp 0 end pmatrix l 3 1 0 0 0 1 0 0 0 0 displaystyle lambda 3 begin pmatrix 1 amp 0 amp 0 0 amp 1 amp 0 0 amp 0 amp 0 end pmatrix l 4 0 0 1 0 0 0 1 0 0 displaystyle lambda 4 begin pmatrix 0 amp 0 amp 1 0 amp 0 amp 0 1 amp 0 amp 0 end pmatrix l 5 0 0 i 0 0 0 i 0 0 displaystyle lambda 5 begin pmatrix 0 amp 0 amp i 0 amp 0 amp 0 i amp 0 amp 0 end pmatrix l 6 0 0 0 0 0 1 0 1 0 displaystyle lambda 6 begin pmatrix 0 amp 0 amp 0 0 amp 0 amp 1 0 amp 1 amp 0 end pmatrix l 7 0 0 0 0 0 i 0 i 0 displaystyle lambda 7 begin pmatrix 0 amp 0 amp 0 0 amp 0 amp i 0 amp i amp 0 end pmatrix l 8 1 3 1 0 0 0 1 0 0 0 2 displaystyle lambda 8 frac 1 sqrt 3 begin pmatrix 1 amp 0 amp 0 0 amp 1 amp 0 0 amp 0 amp 2 end pmatrix Ce ermitovi matrici Slid usih matric l i displaystyle lambda i dorivnyuye nulyu Sp l j 0 displaystyle text Sp lambda j 0 Krim togo Sp l i l j 2 d i j displaystyle text Sp lambda i lambda j 2 delta ij de d i j displaystyle delta i j simvol Kronekera Matrici g i displaystyle g i viznachayutsya yak g i 1 2 l i displaystyle g i frac 1 2 lambda i Komutatori cih matric zadovolnyayut spivvidnoshennya g i g j i f i j k g k displaystyle g i g j if ijk g k de povtorennya indeksu k oznachaye pidsumovuvannya a f i j k displaystyle f ijk povnistyu antisimetrichnij za troma indeksami i maye znachennya f 123 1 f 147 f 165 f 246 f 257 f 345 f 376 1 2 f 458 f 678 3 2 displaystyle f 123 1 quad f 147 f 165 f 246 f 257 f 345 f 376 frac 1 2 quad f 458 f 678 frac sqrt 3 2 Bud yakij element grupi SU 3 mozhe buti zapisanim u formi x e i k 8 k g k displaystyle x e i sum k theta k g k de 8 k displaystyle theta k dijsni chisla Same cya vlastivist oznachaye sho matrici l i displaystyle lambda i a z nimi i g i displaystyle g i ye generatorami grupi Dzherela RedaguvatiAdams Dzh F Lekcii po gruppam Li Nauka 1979 Otrimano z https uk wikipedia org w index php title Matrici Gell Mana amp oldid 38525156
