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., . .: , 1974. 251 c.
( ): simetriyavkvantovoyfizike1974.pdf
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) G()*11' *22 = {(, /); = , + 2 - 2,2) / ^ 0}, (3.2.44)
H^i*22 = {{%', ) : ' = , - / - < < /}.
) G {'" *2 = {(, /) : = Xj + 2 - 2!2, / ^0},
: *22 = {{%', ) : ' = , - / - < < /}.
220 .
(3.1.52)
) 1,
) ?'*22 = 2/ + + 1, (3.2.45)
) d?p"*2p2= - -
/// PlXjpj 222\_
Vp Pi ' 2
= Usu (2) ( ( () 1 ))^ "1+"1+17 X ^2)'(/?(. (, ))-1) Ui
(/? (2! (, ))-1).
/ 1 PlXjPi 222 \
(7' [ ' 22
= t/sii (2) (R ( ()-1 ))^ & ' (/? (,; (, ))-')
XUpJ\?(R(P2, (, ))_1),-"" ".

// ^ _ 111 222\ (3.2.46)
N /' .., ' ". '
PlPl 22
~ a w "\> 1//
'
= C/St/ (R ( ()-1 )) . C/g'ca1 (R ( (, ))_1), X
X t/?(2)2 ( (2; (, 1)^,^
SU (2) (2.2.4),
?(2) - (1.4.3) (2.4.4).

VII. pi = 6(0) + (), 2 = "26(3). ,
. 3.1,
Qvn = {me(0) : m > 0} (J {(3) : n > 0} (J {e(0) + e(3)}. (3.2.47) VII.
1. pi e {me(0) '. m > 0}. G, = ?(2), G2 = SU{\, 1),

G(p) = SU (2), G (p, q) = //,. : a) Pi =(xb pi); HUPl
= {(xj, pi)} ?(2)
) pi = ( pi); Ipi = (('" ,): ' = - < , < 00)
221
. 2 = (2, /2, %)
^1, * = {(2> ^2) ' = *2> - < "2 < }>
^l, v-iU = {(2' ^2) 2 = 2> - (- "I- /^) ^ " /2 " 1}>
(3.1.43)
) *' * = {(, ): = xi+x2-2xix2) - < < },
*'*1" = {(, ) : = , + 2 - 2xiX2)
( + /2) > /2 + 2/2 ([ + xj/2) + 1},
1%*1 = {(, ) : = xi, = pi},
) / _ ((, ) . = [ + 2-2xiX2, - << }, ^ ^
Hi%^h = {{, ): = 1, - < < },
= {(, ) : =
- < ( + ,/2) +1 + ( + /2) - /2 - 2/2 - 1}.
,
G(\, " = Slf{2)", " = {(, /); ' = , / >I + /2 | - /2} (3.2.49)
, (3.1.53),
.a) G {p)K[V"' * = {(', /) : = X) + 2 - 2xjX2, /^0},
*1 / ^ = {(', ): ' = , - / - < < /},
G ()'1' = {(, /) : = Xi + 2 - 2!2,
/ > max (0, /2 + 2/2 (, + ,/2) - /2 + 1)},
H*$i '2 = {(', ): ' = , max (- / - /2, /2 + /2
(, + ,/2) + 1)< ( + /2)</ + /2}, .
(3.2.50)
) G ()*'1'11 = {(, /): = , + 2 - 2,2, / > 0},
*,", _ ^ . / = > _ / _ <^ /}.
222
.
(3.1.52)
)
.,",/20

= 2/ -f- + 1,
,," 22______
/ -
2/ -|- -(- 1
0 ^ ^ - /2 - 2/2 (pi + Xj/2) - x/2 - 1, / + x/2 - /2 - x2/2 T (p[
+ Xj/2)
/ + x/2 ^ - /2 - x2/2 + (p[ + Xj/2) - 1,
0) Uytl = N Q.
-
(3.2.51)
// ) 11
PlXjfXj 22/212
) =
= (( (1 p)U ?(2 ( (Pi; (, )') X ^^; (, ))-1)^-
^.,^,
//
6) ( ,1 ?
PiX,p, 22/212
(3.2.52)
>
11 22
= t/si/ ( ( (p)-'p)U %1' ( (Pi; (, ) V.X
X Usu (V, 2 ( (> (, )) )-, 2-
St/ (2) (2.2.4), ?(2) -
(1.4.13) (2.4.4), SU (1, 1) - (2.3.15).
VII.2. ^ {"6(3): >0}. G{ = E (2), G2 = G () - SU (1, 1),
G(p, q) = Hj. Hp"Pl +.^ , VII. 1 [.
(3.2.48)].
gc^.^sgo, 1 )*.,* =
= {(', /, 0) :' = , / = -(1 +)/2 + /, >0}11 U {(', /, ) : ' = ,
0 ^ ^ | + /2 | - /2 - 1,
= sign ( + /2)}, (3.2.53)
223
(3.1.53)
) G {)*'" *2h0 =
= {(, I, 0) : = Xj + 2 - 2xiX2) / = - (1 + )/2 + ip, ^ 0} (J {(,
I, +) = X] - 2!2, / > 0}
U {(, /, -): = , + 2 - 2xiX2) I ^ 0}>
= {(, /, 0) : X = , + 2 - 2,2) / = - (1 + )/2 + ip, > 0} (J
{(, I, ): -Xi + 2 - 2,2) />0} (J {(, I, ) I = | + 2 -
2!2) 0 ^ ^ - /2 - 2/2 +
+ (Pi + ,/2) - 2}, ,'/'!/1 = {(', ) ; ' = , - < < },
˱ = {(', ): ' = X, ( + /2) >/2 + 2/2
(pi + Xj/2) + 1}, = {(', )'. ' = , ( + /2) ^ / + /2 + 1},
= {(', )' = , ( + /2) ^ max(/ + /2 + 1,
/2 + 2/2 + 1 (, + 2/2))},
^1 = "', ) : ' = , /2 + 2/2 + 1 + (, + ,/2) <
^ dh ( /2) - I - /2 - 1},
) G () *1 = {(, I, 0) : = Xi + 2 - 2xix2,
/ = - (1 + )/2 + ip, 0}U U {(, I, +)'. = Xj + 2 - 2xix2, / ^ 0} (J
11{(, I, -) : = , +2 - 2]2, /^0}, *1 = {(', ) : ' = ,
- < < },
'1 ?hrk = {(', ): ' = X, ( + /2) > / + /2 + 1}.
(3.2.54)
(3.1.52),
) ^"1 =
__ 1 - /-/2- /2-2/2 + (1+1/2)-1 ]2 = -] = ,
_ 1 ,
*iUi\z w (3.2.55)
) -1\ = "1
224
.
-

/ pxlr\ Pl^iHi 22\
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