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相对论、量子力学及其场论的,本质、规律,及其必然且必需的发展(37)
2线可变基矢的微分、偏微分:
(接(36))
d[基矢X(xy)]=(d[基矢X(x)])叉乘[基矢X(y)] + [基矢X(x)]叉乘(d[基矢X(y)]) =-[([dl(A,a’)w(Ax’,xa’)[基矢X(x’)])叉乘[基矢X(y)], a’, x’=0到3求和]
-[[基矢X(x)]叉乘([dl(A,a’)w(Ay’,ya’)[基矢X(y’)]), a’, y’=0到3求和]
=-[dl(A,a’)(w(Ax’,xa’)[基矢X(x’y)]
+w(Ay’,ya’)[基矢X(xy’)]),a’,x’,y’=0到3求和]。
d[基矢X(xy)]/dt(X) =-[(dt(A)/dt(X))dl(A,a’)/dt(A)
(w(Ax’,xa’)[基矢X(x’y)]
+w(Ay’,ya’)[基矢X(xy’)]),a’,x’,y’=0到3求和]
=[(dt(A)/dt(X))dl(A,a’)/dt(A)
(w(Ax,x’a’)+w(Ay,y’a’))[基矢X(xy)],a’,x’,y’=0到3求和]。
(偏分l(A,a’)[基矢X(xy)]=[w(Axy,x’y’a’)[基矢X(xy)],a’,x’,y’=0到3求和], xy=01,02,03,23,31,12,
w(Axy,x’y’a’)=w(Ax,x’a’)+w(Ay,y’a’), a=0,1,2,3, xy,x’y’=01,02,03,23,31,12,
(未完待续)
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