where
Q(|Zl|,|i?2|) = = (T,\^\\E1+lzJ^\\E1+izJ^a\\E-
i
(^11^11^4.,^iiJKIU.z- .1Kb--
\*—r
1+iz
\ 2\
x p-1/2
••IkinlUJ
x 3/2-p
•lkJ|£)
MAXWELL - DIRAC EQUATIONS 47
(2.104)
If |Zi| - |Z2| - 0 , then
0(0,0) ( ^ | K I U
l
I K I U
i
| K I U - - - | K b )
P
"
1 / 2
(2.105a)
/ V ^ \ 3/2-p
( Z^ IK IblK H^ \\ui3 \\E ||ttin ||SJ
If \Zi\ IZ2I 1, then 1 + |Zi| |Z|, so it follows from the second inequality of
Corollary 2.6 that
Q(|Z
1
|,|Z
2
|)c(^||
W i l
||
B i + | z |
|K||
B i
|K||
E
---||
W i
J|
E
)^
1 / 2
(2.105b)
i
/ v - ^ \ 3/2-p
(5
l l
^
i l
^iz,ll^kll
u
*3lb---IKIU ) , |Zi| = |2
2
|i .
If |Zi| \Z2\, then |Zi| + 1 |Z2|, so it follows from Corollary 2.6 that
Q(|^i|,|Z
2
|)c(X)|K||
1 +
|
Z
||K||
B i
||u
i
,||
B
-..||«i
B
lb)''~
1 / 2
(2.105c)
i
/\—v \ 3/2-p
It follows from inequalities (2.103) and (2.105) that
WTxFzl ®T%)Tn(®]=lUj)\\E (2.106)
^
Cn,|z|
( 2 ^ ll^ix
WE1+]Z]
\\ui2
WE,
I K
WE'"
I K
WE)
i
/ V ^ \ 3/2-p
{ 2_s 11^* 1 H^zi
HWi2
K '1^3 lb
\\uin
WE)
i
where \ZX\ + \Z2\ = |Z|. Inequalities (2.100) and (2.106) show that
||l£(l£
®Tnzl)rn{®^=1uj)\\EN
(2.107)
/ V ^ \ 3/2-p
Cjv,n,|z| ( 2^ IK lbN+|z| IK lb, IK WE'" I K lbJ
i
(Eiiu*iii^+lzi+JiUi"iifiJitti»^"-iiu*-^)'"1/2'
^ - ^
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