||
4维时空,自旋力、 [1线矢]、[3线矢]=[1*线矢]
A(4)[1线矢]叉乘B(4)[1线矢]=C(6)[2线矢]
={iA0[0矢]+Aj[j矢],j=1到3求和}
叉乘{iB0[0矢]+Bj[j矢],j=1到3求和}
={i(A0Bj-AjB0)[0j矢]+(AkBl-AlBk)[kl矢]
,jkl=123循环求和},
对A(4)[标量]的4维时空偏分[1线矢]=偏(4)A(4)[1线矢]
={(-i偏(4)A(4)/偏r(4)0)[0矢]
+(偏(4)A(4)j/偏r(4)j)[j矢] ,j=1到3求和}
={-i(偏(4)A(4)/偏r0)[0矢]+(偏(3)A(3)/偏r(3))[(3)矢]},
偏(4)[1线矢]
={(-i偏(4)/偏r(4)0)[0矢]+(偏(4)/偏r(4)j)[j矢] ,j=1到3求和}
={-i(偏(4)/偏r0)[0矢]+(偏(3)/偏r(3))[(3)矢]},
r0=c t或a*t, 量纲:[L]^(-1),
对于电中性粒子,
p(4)[矢]=m0(c或a*){i(c或a*)[0矢]+v(3)[(3)矢]}
/[(c或a*)^2-v(3)^2]^(1/2),
6维时空自旋[2线矢]=s(6)[ 2线矢]
=偏(4)[ 1线矢]叉乘p(4)[ 1线矢]
={(dp4,j/dr4,0-dp4,0/dr4,j)[0j矢]
+(dp4,l/dr4,k-dp4,k/dr4,l)[kl矢] ,jkl=123循环求和}
=m0(c或a*)
{[i(dv4,j/d(a*t声或c t光)-d(a*或c)/dr4,j)[0j矢]
+(dv4,l/dr4,k-dv4,k/dr4,l)[kl矢] ,jkl=123循环求和]
[(c或a*)^2-v(3)^2]
+[i(v4,jdv4,j/d(a*t声或c t光)-(a*或c)d/dr4,j)[0j矢]
+(v4,ldv4,l/dr4,k-v4,kdv4,k/dr4,l)[kl矢]
,jkl=123循环求和]}/[(c或a*)^2-v(3)^2]^(3/2),
量纲:[M][T]^(-1),
4维时空自旋力[1线矢]:
f(4)自旋力[1线矢]=v(4)[1线矢]点乘 6维时空自旋[2线矢]
={v4,j(dp4,j/dr4,0-dp4,j/dr4,0)[0矢]
-v4,0(dp4,j/dr4,0-dp4,j/dr4,0)[j矢]
+v4,l(dp4,l/dr4,k-dp4,k/dr4,l)[k矢]
-v4,k(dp4,l/dr4,k-dp4,k/dr4,l)[l矢]
,jkl=123循环求和}
=3维空间的,f(3)运动[1线矢]+f(3)离心[1线矢]
=m0(c或a*)
{[-i(a*或c)(dv4,j/((a*或c)dt) -d(a*或c)/dr4,j)[j矢]
+iv4,j(dv4,j/((a*或c)dt)-d(a*或c)/dr4,j)[0矢]
-v4,k(dv4,l/dr4,k-dv4,k/dr4,l)[l矢]
+v4,l(dv4,l/dr4,k-dv4,k/dr4,l)[k矢] ,jkl=123循环求和]
[(c或a*)^2-v(3)^2]
+[-i(a*或c)(v4,jdv4,j/((a*或c)dt)
-(a*或c)d(a*或c)/dr4,j)[j矢]
+iv4,j(v4,jdv4,j/((a*或c)dt)
-(a*或c)d(a*或c)/dr4,j)[0矢]
-v4,k(v4,ldv4,l/dr4,k-v4,kdv4,k/dr4,l)[l矢]
+v4,l(v4,ldv4,l/dr4,k-v4,kdv4,k/dr4,l)[k矢]
,jkl=123循环求和]}/[(c或a*)^2-v(3)^2]^(3/2),
4维时空自旋力[3线矢]:
f(4)自旋[3线矢]=v(4)[1线矢]叉乘 6维时空自旋[2线矢]
=v(4)[1线矢]叉乘 s(6)[ 2线矢]
={v4,j(dp4,l/dr4,k-dp4,k/dr4,l)[0*矢]
+v4,0(dp4,l/dr4,k-dp4,k/dr4,l)[j*矢]
-v4,l(dp4,j/dr4,0-dp4,0/dr4,j)[k*矢]
+v4,k(dp4,j/dr4,0-dp4,0/dr4,j)[l*矢]
,jkl=123循环求和}
=3维空间的,f(3)运动[1*线矢]+f(3)离心[1*线矢]
=m0(c或a*)
{[iv4,k(dv4,l/((a*或c)dt)-d(a*或c)/dr4,l)[0kl矢]]
+v4,j(dv4,l/dr4,k-dv4,k/dr4,l)[kl矢] ,jkl=123循环求和]
[(c或a*)^2-v(3)^2]
+[iv4,k(v4,ldv4,l/((a*或c)dt)-(a*或c)d/dr4,l)[0kl矢]
+v4,j(v4,ldv4,l/dr4,k-v4,kdv4,k/dr4,l)[jkl矢]
,jkl=123循环求和]}/[(c或a*)^2-v(3)^2]^(3/2),
((声传)m0不=0,v4,0=a*,r4,0=a*t声,
(光传)m0不=0,v4,0=c,r4,0=c t光,)
量纲:[M][L][T]^(-2),C(4)[1线矢]=A(4)[1线矢]点乘B(6)[2线矢],
C(4)[3线矢]=C(4)[1*线矢]=A(4)[1线矢]叉乘B(6)[2线矢],
C(4)[1*线矢]与A(4)[1线矢]、B(6)[2线矢],都正交,
C(4)[1线矢]与C(4)[1*线矢],彼此正交。
对于声子或光子, f(4)自旋力[1线矢]=0/0,也只能分别表达为:d(m0a*)/dt声 或 d(m0c)/dt光
或d(h声频率)/dr(4)=hz声或d(h光频率)/dr(4)=hz光,
z声、z光,分别是,声、光,沿时轴或空间轴的红移量,
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