Почему дубровский стал разбойником rhfnrfz bcnjhbz;pdf

¨¸Ó³ ¢ —Ÿ. 2014. ’. 11, º 6(190). ‘. 1118Ä1121
”ˆ‡ˆŠ ‹…Œ…’›• —‘’ˆ– ˆ ’Œƒ Ÿ„. ’…ˆŸ
‹…Š’ˆ—…‘ŠŸ ˆ Œƒˆ’Ÿ
‹Ÿˆ‡“…Œ‘’ˆ ’—…—„›• —‘’ˆ–
‘ ‘ˆŒ 1/2
. Ÿ. ‘¨²¥´±μ1
¡Ñ¥¤¨´¥´´Ò° ¨´¸É¨ÉÊÉ Ö¤¥·´ÒÌ ¨¸¸²¥¤μ¢ ´¨°, „Ê¡´ ˆ´¸É¨ÉÊÉ Ö¤¥·´ÒÌ ¶·μ¡²¥³ ¥²μ·Ê¸¸±μ£μ £μ¸Ê¤ ·¸É¢¥´´μ£μ Ê´¨¢¥·¸¨É¥É , Œ¨´¸±
²¥±É·¨Î¥¸± Ö ¨ ³ £´¨É´ Ö ¶μ²Ö·¨§Ê¥³μ¸É¨ ÉμÎ¥Î´μ¶μ¤μ¡´ÒÌ Î ¸É¨Í ¸μ ¸¶¨´μ³ 1/2, ¨³¥ÕÐ¨Ì ´μ³ ²Ó´Ò° ³ £´¨É´Ò° ³μ³¥´É, · ¸¸Î¨É ´Ò ¶ÊÉ¥³ ¶·¥μ¡· §μ¢ ´¨Ö ¨¸Ìμ¤´μ£μ £ ³¨²ÓÉμ´¨ ´ ± ¶·¥¤¸É ¢²¥´¨Õ ”μ²¤¨Ä‚ ÊÉÌμ°§¥´ . ·μ¨§¢¥¤¥´μ ¸· ¢´¥´¨¥ ¸μμÉ¢¥É¸É¢ÊÕÐ¨Ì ·¥§Ê²ÓÉ Éμ¢ ¤²Ö
Î ¸É¨Í ¸μ ¸¶¨´ ³¨ 1/2 ¨ 1.
Electric and magnetic polarizabilities of pointlike spin-1/2 particles possessing an anomalous magnetic moment are calculated with the transformation of an initial Hamiltonian to the FoldyÄWouthuysen
representation. Comparison of corresponding results for spin-1/2 and spin-1 particles is performed.
PACS: 03.65.Pm; 11.10.Ef; 12.20.Ds
‚ ´ ¸ÉμÖÐ¥° · ¡μÉ¥ ³Ò μ¶·¥¤¥²Ö¥³ Ô²¥±É·¨Î¥¸±ÊÕ ¨ ³ £´¨É´ÊÕ ¶μ²Ö·¨§Ê¥³μ¸É¨ ÉμÎ¥Î´μ¶μ¤μ¡´ÒÌ Î ¸É¨Í ¸μ ¸¶¨´μ³ 1/2, ¨³¥ÕÐ¨Ì ´μ³ ²Ó´Ò° ³ £´¨É´Ò° ³μ³¥´É (ŒŒ),
¶ÊÉ¥³ ¨¸¶μ²Ó§μ¢ ´¨Ö ¶·¥μ¡· §μ¢ ´¨Ö ”μ²¤¨Ä‚ ÊÉÌμ°§¥´ (”‚).
“´¨± ²Ó´Ò¥ ¸¢μ°¸É¢ ¶·¥¤¸É ¢²¥´¨Ö ”‚ [1] ¤¥² ÕÉ ¥£μ ¢¥¸Ó³ Ê¤μ¡´Ò³ ¤²Ö ¶¥·¥Ìμ¤ ± ±¢ §¨±² ¸¸¨Î¥¸±μ³Ê ¶·¨¡²¨¦¥´¨Õ ¨ ´ Ìμ¦¤¥´¨Ö ±² ¸¸¨Î¥¸±μ£μ ¶·¥¤¥² ·¥²ÖÉ¨¢¨¸É¸±μ° ±¢ ´Éμ¢μ° ³¥Ì ´¨±¨. „ ¦¥ ¤²Ö ·¥²ÖÉ¨¢¨¸É¸±¨Ì Î ¸É¨Í ¢μ ¢´¥Ï´¥³ ¶μ²¥ μ¶¥· Éμ·Ò ¢ ¤ ´´μ³ ¶·¥¤¸É ¢²¥´¨¨ ¶μ²´μ¸ÉÓÕ ´ ²μ£¨Î´Ò ¸μμÉ¢¥É¸É¢ÊÕÐ¨³ μ¶¥· Éμ· ³
´¥·¥²ÖÉ¨¢¨¸É¸±μ° ±¢ ´Éμ¢μ° ³¥Ì ´¨±¨. ‚ Î ¸É´μ¸É¨, μ¶¥· Éμ·Ò ¶μ²μ¦¥´¨Ö (ÓÕÉμ´ Ä
‚¨£´¥· ) [2] ¨ ¨³¶Ê²Ó¸ · ¢´Ò r ¨ p = −i∇, μ¶¥· Éμ· ¶μ²Ö·¨§ Í¨¨ ¤²Ö Î ¸É¨Í ¸μ
¸¶¨´μ³ 1/2 ¢Ò· ¦ ¥É¸Ö ¤¨· ±μ¢¸±μ° ³ É·¨Í¥° Π. ‚ ¤·Ê£¨Ì ¶·¥¤¸É ¢²¥´¨ÖÌ ÔÉ¨ μ¶¥· Éμ·Ò μ¶·¥¤¥²ÖÕÉ¸Ö §´ Î¨É¥²Ó´μ ¡μ²¥¥ £·μ³μ§¤±¨³¨ Ëμ·³Ê² ³¨ (¸³. [1, 3]). μ³¨³μ
¶·μ¸Éμ£μ ¨ μ¤´μ§´ Î´μ£μ ¢¨¤ μ¶¥· Éμ·μ¢, ¸μμÉ¢¥É¸É¢ÊÕÐ¨Ì ±² ¸¸¨Î¥¸±¨³ ´ ¡²Õ¤ ¥³Ò³,
¢ ¦´¥°Ï¨³ ¤μ¸Éμ¨´¸É¢μ³ ¶·¥¤¸É ¢²¥´¨Ö ”‚ Ö¢²Ö¥É¸Ö ¢μ¸¸É ´μ¢²¥´¨¥ ¢¥·μÖÉ´μ¸É´μ° ¨´É¥·¶·¥É Í¨¨ ¢μ²´μ¢μ° ËÊ´±Í¨¨. μ¸±μ²Ó±Ê, ± ± Ê± § ´μ ¢ÒÏ¥, ¨³¥´´μ ¢ ¶·¥¤¸É ¢²¥´¨¨
”‚ μ¶¥· Éμ· ÓÕÉμ´ Ä‚¨£´¥· , Ì · ±É¥·¨§ÊÕÐ¨° ¶μ²μ¦¥´¨¥ £¥μ³¥É·¨Î¥¸±μ£μ Í¥´É· Î ¸É¨ÍÒ, · ¢¥´ · ¤¨Ê¸-¢¥±Éμ·Ê r, Éμ ±¢ ¤· É ³μ¤Ê²Ö ¢μ²´μ¢μ° ËÊ´±Í¨¨ μ¶·¥¤¥²Ö¥É ¶²μÉ´μ¸ÉÓ ¢¥·μÖÉ´μ¸É¨ ´ Ìμ¦¤¥´¨Ö Î ¸É¨ÍÒ ¢ ÉμÎ±¥ ¸ ¤ ´´Ò³ · ¤¨Ê¸-¢¥±Éμ·μ³. É³¥É¨³, ÎÉμ
1 E-mail:
[email protected]
²¥±É·¨Î¥¸± Ö ¨ ³ £´¨É´ Ö ¶μ²Ö·¨§Ê¥³μ¸É¨ ÉμÎ¥Î´μ¶μ¤μ¡´ÒÌ Î ¸É¨Í ¸μ ¸¶¨´μ³ 1/2 1119
¢ ¶·¥¤¸É ¢²¥´¨¨ ”‚ £ ³¨²ÓÉμ´¨ ´ ¨ ¢¸¥ μ¶¥· Éμ·Ò ¤¨ £μ´ ²Ó´Ò ¶μ ¤¢Ê³ ¸¶¨´μ· ³ (¡²μ±¤¨ £μ´ ²Ó´Ò). ˆ¸¶μ²Ó§μ¢ ´¨¥ ÔÉμ£μ ¶·¥¤¸É ¢²¥´¨Ö Ê¸É· ´Ö¥É ¢μ§³μ¦´μ¸ÉÓ ¶μÖ¢²¥´¨Ö ´¥μ¤´μ§´ Î´μ¸É¥° ¶·¨ ·¥Ï¥´¨¨ § ¤ Î¨ ´ Ìμ¦¤¥´¨Ö ±² ¸¸¨Î¥¸±μ£μ ¶·¥¤¥² ·¥²ÖÉ¨¢¨¸É¸±μ°
±¢ ´Éμ¢μ° ³¥Ì ´¨±¨ [1, 4].
Š ´ ¨¡μ²¥¥ ¢ ¦´Ò³ ¶¥· ³¥É· ³, Ì · ±É¥·¨§ÊÕÐ¨³ Î ¸É¨ÍÒ ¨ Ö¤· , ¶·¨´ ¤²¥¦ É
¸± ²Ö·´Ò¥ Ô²¥±É·¨Î¥¸± Ö ¨ ³ £´¨É´ Ö ¶μ²Ö·¨§Ê¥³μ¸É¨. ˆÌ ¢±² ¤ ¢ £ ³¨²ÓÉμ´¨ ´ ¢ ¶·¥¤¸É ¢²¥´¨¨ ”‚ μ¶·¥¤¥²Ö¥É¸Ö ¢Ò· ¦¥´¨¥³
1
1
ΔHFW = − αs E 2 − βs B 2 .
2
2
(1)
ŒÒ · ¸¸³ É·¨¢ ¥³ ¸²ÊÎ ° ¸É Í¨μ´ ·´ÒÌ ¨ μ¤´μ·μ¤´ÒÌ Ô²¥±É·¨Î¥¸±μ£μ (E) ¨ ³ £´¨É´μ£μ (B) ¶μ²¥° ¨ ¨¸¶μ²Ó§Ê¥³ ¸¨¸É¥³Ê ¥¤¨´¨Í = 1, c = 1.
…¸²¨ ¢ ±² ¸¸¨Î¥¸±μ° Ë¨§¨±¥ Î ¸É¨Í ³μ¦¥É ¨³¥ÉÓ ´¥´Ê²¥¢Ò¥ ¶μ²Ö·¨§Ê¥³μ¸É¨ Éμ²Ó±μ
¶·¨ ´ ²¨Î¨¨ Ê ´¥¥ ¢´ÊÉ·¥´´¥° ¸É·Ê±ÉÊ·Ò, Éμ ¢ ±¢ ´Éμ¢μ° ³¥Ì ´¨±¥ μ´¨ ¶μÖ¢²ÖÕÉ¸Ö ¤ ¦¥
Ê ÉμÎ¥Î´μ¶μ¤μ¡´ÒÌ μ¡Ñ¥±Éμ¢. ¶·¥¤¥²¨ÉÓ ÔÉ¨ ¶ · ³¥É·Ò ¶μ§¢μ²Ö¥É ¶·¥μ¡· §μ¢ ´¨¥ ”‚
¨¸Ìμ¤´μ£μ Ê· ¢´¥´¨Ö „¨· ± Ä Ê²¨ [5] ¤²Ö Î ¸É¨Í ¸ ŒŒ ¸ ¶μ¸²¥¤ÊÕÐ¨³ ¶¥·¥Ìμ¤μ³
± ±² ¸¸¨Î¥¸±μ³Ê ¶·¥¤¥²Ê. ¤´ ±μ ¤²Ö ·¥Ï¥´¨Ö ¤ ´´μ° § ¤ Î¨ ´¥μ¡Ìμ¤¨³μ ¢ÒÎ¨¸²¥´¨¥
¸² £ ¥³ÒÌ, ±¢ ¤· É¨Î´ÒÌ ¶μ ¢´¥Ï´¥³Ê ¶μ²Õ. É ¶·μÍ¥¤Ê· É·¥¡Ê¥É μ¶·¥¤¥²¥´´μ° μ¸Éμ·μ¦´μ¸É¨, ¶μ¸±μ²Ó±Ê · §´Ò¥ ³¥Éμ¤Ò ¶·¨¢μ¤ÖÉ ± · §²¨Î´Ò³ ·¥§Ê²ÓÉ É ³ (¸³. μ¡§μ· [6] ¨
¸¸Ò²±¨ É ³). Š ¶· ¢¨²Ó´Ò³ ·¥§Ê²ÓÉ É ³ ¶·¨¢μ¤¨É ¨¸¶μ²Ó§μ¢ ´¨¥ ³¥Éμ¤ ·¨±¸¥´ [7].
ˆ¸Ìμ¤´Ò° £ ³¨²ÓÉμ´¨ ´ „¨· ± Ä Ê²¨ [5] Ê¤μ¡´μ · §¤¥²¨ÉÓ ´ Î¥É´Ò¥ ¨ ´¥Î¥É´Ò¥ ¸² £ ¥³Ò¥, ±μ³³ÊÉ¨·ÊÕÐ¨¥ ¨ ´É¨±μ³³ÊÉ¨·ÊÕÐ¨¥ ¸ ¤¨· ±μ¢¸±μ° ³ É·¨Í¥° β ¸μμÉ¢¥É¸É¢¥´´μ:
HD = βm + E + O,
βE = Eβ,
βO = −Oβ.
(2)
‡¤¥¸Ó
E = eΦ − μ Π · B,
O = cα · π + iμ γ · E,
(3)
£¤¥ μ Å ŒŒ. ŒÒ ¨¸¶μ²Ó§Ê¥³ μ¡ÒÎ´Ò¥ μ¡μ§´ Î¥´¨Ö [8] ¤²Ö ¤¨· ±μ¢¸±¨Ì ³ É·¨Í.
§²μ¦¥´¨¥ £ ³¨²ÓÉμ´¨ ´ ¢ ¶·¥¤¸É ¢²¥´¨¨ ”‚ ¶μ ¸É¥¶¥´Ö³ 1/m, ¶μ²ÊÎ¥´´μ¥ ³¥Éμ¤μ³ ·¨±¸¥´ , ¶·¨¢¥¤¥´μ ¢ · ¡μÉ Ì [6, 9, 10]. ‚ ´ ²¨§¨·Ê¥³μ³ ¸²ÊÎ ¥ ¸² £ ¥³Ò¥,
¶·μ¶μ·Í¨μ´ ²Ó´Ò¥ Î¥É¢¥·Éμ° ¨ ¡μ²¥¥ ¢Ò¸μ±¨³ ¸É¥¶¥´Ö³ μ¡· É´μ° ³ ¸¸Ò, ³μ¦´μ ´¥ ÊÎ¨ÉÒ¢ ÉÓ. ‚ ÔÉμ³ ¸²ÊÎ ¥ £ ³¨²ÓÉμ´¨ ´ ¢ ¶·¥¤¸É ¢²¥´¨¨ ”‚ μ¶·¥¤¥²Ö¥É¸Ö Ê· ¢´¥´¨¥³
O4
O2
β
1
−
[O, [O, F ]] +
{O, [[O, F ], F ]} , (4)
HFW = β m +
+E −
2m 8m3
8m2
16m3
£¤¥ F = E − i∂/∂t. „²Ö · ¸¸³ É·¨¢ ¥³μ° ¸É Í¨μ´ ·´μ° § ¤ Î¨ F = E.
¸Î¥É ¶μ Ëμ·³Ê² ³ (3), (4) ¶·¨¢μ¤¨É ± ¸²¥¤ÊÕÐ¥³Ê ¢Ò· ¦¥´¨Õ:
HFW
π4
π2
1 μ0
(2Σ · [π × E] − ∇ · E) −
−
+
μ
=β m+
+
eΦ
+
2m 8m3
2m 2
μ
(μ0 + μ )μ 2
μ20 2
− (μ0 + μ ) Π · B +
E
B , (5)
{Π
·
π,
π
·
B}
+
β
−
β
4m2
2m
2m
£¤¥ μ0 = e/(2m) Å ¤¨· ±μ¢¸±¨° ³ £´¨É´Ò° ³μ³¥´É.
1120 ‘¨²¥´±μ . Ÿ.
É³¥É¨³, ÎÉμ ¶μ¸²¥¤´¥¥ ¸² £ ¥³μ¥ ¢ Ê· ¢´¥´¨¨ (4) ´¥ ¢´μ¸¨É ¢±² ¤ ¢ Ô²¥±É·¨Î¥¸±ÊÕ
¨ ³ £´¨É´ÊÕ ¶μ²Ö·¨§Ê¥³μ¸É¨. ¸Î¥É ¸ ¶μ³μÐÓÕ ³¥Éμ¤ , ¶·¥¤²μ¦¥´´μ£μ ¢ μ·¨£¨´ ²Ó´μ° · ¡μÉ¥ ”μ²¤¨ ¨ ‚ ÊÉÌμ°§¥´ [1], ¨ ¤·Ê£¨Ì ¨É¥· Í¨μ´´ÒÌ ³¥Éμ¤μ¢ (¸³. [10, 11] ¨
¸¸Ò²±¨ É ³) ¶·¨¢μ¤¨É ± ¨´μ³Ê ¢¨¤Ê ÔÉμ£μ ¸² £ ¥³μ£μ ¨, ± ± ¸²¥¤¸É¢¨¥, ´¥ ¤ ¥É ¶· ¢¨²Ó´μ£μ ¢Ò· ¦¥´¨Ö ¤²Ö Ô²¥±É·¨Î¥¸±μ° ¶μ²Ö·¨§Ê¥³μ¸É¨. ‘· ¢´¥´¨¥ Ê· ¢´¥´¨° (1) ¨ (5)
¶μ± §Ò¢ ¥É, ÎÉμ ¸± ²Ö·´Ò¥ Ô²¥±É·¨Î¥¸± Ö ¨ ³ £´¨É´ Ö ¶μ²Ö·¨§Ê¥³μ¸É¨ ÉμÎ¥Î´μ¶μ¤μ¡´ÒÌ
Î ¸É¨Í, μ¡² ¤ ÕÐ¨Ì ŒŒ, ¨³¥ÕÉ ¢¨¤
αS = −
e2 g(g − 2)
(μ0 + μ )μ
=−
,
m
16m3
βS =
e2
μ20
=
.
m
4m3
(6)
Œ É·¨ÍÊ β ³μ¦´μ μ¶Ê¸É¨ÉÓ, ¶μ¸±μ²Ó±Ê ¢ ¶·¥¤¸É ¢²¥´¨¨ ”‚ ´¨¦´¨° ¸¶¨´μ· · ¢¥´ ´Ê²Õ.
‚ ¦´Ò³ Ö¢²Ö¥É¸Ö ¸· ¢´¥´¨¥ ¶μ²Ö·¨§Ê¥³μ¸É¥° ÉμÎ¥Î´μ¶μ¤μ¡´ÒÌ Î ¸É¨Í ¸μ ¸¶¨´ ³¨ 1/2
¨ 1. — ¸É¨ÍÒ ¸μ ¸¶¨´μ³ 1 Ì · ±É¥·¨§ÊÕÉ¸Ö ´¥ Éμ²Ó±μ ¸± ²Ö·´Ò³¨, ´μ ¨ É¥´§μ·´Ò³¨ ¶μ²Ö·¨§Ê¥³μ¸ÉÖ³¨, · ¸¸Î¨É ´´Ò³¨ ¢ [12]. ‘± ²Ö·´Ò¥ ¶μ²Ö·¨§Ê¥³μ¸É¨ É ±¨Ì Î ¸É¨Í μ¶·¥¤¥²ÖÕÉ¸Ö ¢Ò· ¦¥´¨Ö³¨ [12]:
αS = −
e2 (g − 1)2
,
m3
βS = 0.
(7)
’ ±¨³ μ¡· §μ³, ¸± ²Ö·´ Ö ³ £´¨É´ Ö ¶μ²Ö·¨§Ê¥³μ¸ÉÓ Î ¸É¨Í ¸μ ¸¶¨´μ³ 1 · ¢´ ´Ê²Õ,
¸± ²Ö·´ Ö Ô²¥±É·¨Î¥¸± Ö ¶μ²Ö·¨§Ê¥³μ¸ÉÓ μÉ²¨Î´ μÉ ´Ê²Ö ¤²Ö Î ¸É¨Í ´¥ Éμ²Ó±μ ¸ ´μ³ ²Ó´Ò³, ´μ ¨ ¸ ´μ·³ ²Ó´Ò³ (g = 2) ³ £´¨É´Ò³ ³μ³¥´Éμ³. É¨ ¸¢μ°¸É¢ μÉ²¨Î ÕÉ¸Ö μÉ
¸μμÉ¢¥É¸É¢ÊÕÐ¨Ì ¸¢μ°¸É¢ Î ¸É¨Í ¸μ ¸¶¨´μ³ 1/2.
É³¥É¨³, ÎÉμ ¸± ²Ö·´Ò¥ ¶μ²Ö·¨§Ê¥³μ¸É¨ ÉμÎ¥Î´μ¶μ¤μ¡´ÒÌ Î ¸É¨Í ¸μ ¸¶¨´μ³ 0 · ¢´Ò
´Ê²Õ (¸³. [13]).
¡μÉ ¶μ¤¤¥·¦ ´ £· ´Éμ³ ¥²μ·Ê¸¸±μ£μ ·¥¸¶Ê¡²¨± ´¸±μ£μ Ëμ´¤ ËÊ´¤ ³¥´É ²Ó´ÒÌ
¨¸¸²¥¤μ¢ ´¨°.
‘ˆ‘Š ‹ˆ’…’“›
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Limit // Phys. Rev. 1950. V. 78. P. 29Ä36.
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V. 21. P. 400Ä406.
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V. 63. P. 1119Ä1121.
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232.
6. de Vries E. FoldyÄWouthuysen Transformations and Related Problems // Fortschr. Phys. 1970.
V. 18. P. 149Ä182.
7. Eriksen E. FoldyÄWouthuysen Transformation. Exact Solution with Generalization to the TwoParticle Problem // Phys. Rev. 1958. V. 111. P. 1011Ä1016.
8. ¥·¥¸É¥Í±¨° ‚. ., ‹¨ËÏ¨Í …. Œ., ¨É ¥¢¸±¨° ‹. . Š¢ ´Éμ¢ Ö Ô²¥±É·μ¤¨´ ³¨± . 3-¥ ¨§¤. Œ.:
Ê± , 1989. 720 ¸.
²¥±É·¨Î¥¸± Ö ¨ ³ £´¨É´ Ö ¶μ²Ö·¨§Ê¥³μ¸É¨ ÉμÎ¥Î´μ¶μ¤μ¡´ÒÌ Î ¸É¨Í ¸μ ¸¶¨´μ³ 1/2 1121
9. de Vries E., Jonker J. E. Non-Relativistic Approximations of the Dirac Hamiltonian // Nucl. Phys.
B. 1968. V. 6. P. 213Ä225.
10. ‘¨²¥´±μ . Ÿ. ‘· ¢´¨É¥²Ó´Ò° ´ ²¨§ ³¥Éμ¤μ¢ ¶·Ö³μ£μ ¨ ®Ï £ § Ï £μ³¯ ¶·¥μ¡· §μ¢ ´¨Ö
”μ²¤¨Ä‚ ÊÉÌμ°§¥´ // ’Œ”. 2013. T. 176. C. 189Ä204.
11. Neznamov V. P., Silenko A. J. FoldyÄWouthuysen Wave Functions and Conditions of Transformation
between Dirac and FoldyÄWouthuysen Representations // J. Math. Phys. 2009. V. 50. P. 122302.
12. Silenko A. J. Quantum-Mechanical Description of Spin-1 Particles with Electric Dipole Moments //
Phys. Rev. D. 2013. V. 87. P. 073015.
13. ‘¨²¥´±μ . Ÿ. ¶¥· Éμ· ƒ ³¨²ÓÉμ´ ¨ ±¢ §¨±² ¸¸¨Î¥¸±¨° ¶·¥¤¥² ¤²Ö ¸± ²Ö·´ÒÌ Î ¸É¨Í ¢ Ô²¥±É·μ³ £´¨É´μ³ ¶μ²¥ // ’Œ”. 2008. T. 156. C. 398Ä411.
μ²ÊÎ¥´μ 11 ³ ·É 2014 £.

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