Документ взят из кэша поисковой машины. Адрес оригинального документа : http://nuclphys.sinp.msu.ru/mirrors/2001_5b.pdf Дата изменения: Tue Jan 13 10:12:37 2009 Дата индексирования: Tue Oct 2 00:06:56 2012 Кодировка: Поисковые слова: m 2

. .




VACUUM IN MODERN QUANTUM THEORY
A. P. MARTYNENK O

In quantum vacuum, it is probable to detect a non-zero energy during an arbitrary short time interval. Energy of the vacuum can manifest itself in either spontaneous creation/annihilation of particles and related antiparticles, or in the emergence/disappearance of electric or chromoelectric field. This article describes the fundamental role played by the concept of vacuum in the quantum theory. . . , .

, , . . , . , . . , () . : , .. () . - , , [1]: E t -- . 2 (1)

www .issep.rssi.ru

86

©

, , - . . , . , , . , , - . . [2].

.., 2001

, 7, 5, 2001



. (), , 1 W = ----8 n = 0. k

W 0 = -2


V

( E 2 + H 2 ) dV ,

(2)


k

.
k

(7)

E, H A : 1 A E = ­ -- ------ , c t H = rot A . (3)

A=


k

A (t )e k

ik r

+ A* ( t ) e k

ik r



(4)

( k , V = 1), W [3]:

W0 , W0 . , 0. 0, , . , . . , , . , E (1) t. , Q. . . = e2 /( c) 1/137,036. , , , - , , . , . , (, . 1), Q r. , - , -

W=


k

2 2 2 | A 'k | k | Ak | ----------2 + --------------- . 8 8c

(5)

, . A k , A 'k ­ , 1 / ( 4 c ) ­ .
2

= / m = ck ( = k2 /(4)).
k

(5) , ­ . , k . . : W=


k

1 n + -- , k 2 k

(6)

n ­ (k

) k . ()

..

87



. , . . , , E vac H vac . (), , m r = eE
vac

Q

,

(10)

r ­ .
. 1. Q

E

vac

=


k

E k cos t ,
k

(11)

(r re = /(mc) ­ ) (r re) [4]: Q Q re - ( r ) ­ --- ------- ln --- , r r r 2r Q Q ( r ) ­ --- ------- exp ­ ---- , re r r r r re , re . (8) (9)

= kc . (10), k e r = ­ --m


k

E k cos t k ----------------------- . 2
k

(12)

, . , ( /(mec)) , : ln (re / r) 1. , (8) (9) . , , , . . , (6), ­ [3]. ­ . (), , . , .

r 0, : e ( r ) = --------2 2m
2 2


k

Ek ----- . 4
k

2

(13)

, (7): 1 W = ----- E 4


V

2 vac

dV =


k

1 -- . 2k

(14)

(11) (14) 4 2 k E k = ---------------- , V (15)


2 2 e -( r ) = ----- ------V m3 2


k

1 ----- . 3
k

(16)




k

dk 2 V ------------ . 3 (2)



88

, 7, 5, 2001



2 . ( r ) :
2 2 ( r ) = -- ------ mc 2 2

|(0) | 2 = m3(Z)3 /(n3), (21) n ( r ) . Evac n = 2 1000 . n = 2: 2S1/2 2P1/2 (S, P l = 0, 1, 1/2 ­ j = l + s ( s ­ , l ­ ). , , , . 2S1/2 2P1/2 . . . 1947 . , , ( ). , -. . , ( r ) , , -, t . 1928 ... , [2]. , , . : , . , ( ) : E = ± p 2 c + m c
2 24

-



d ------ .

(17)

? , , , k < mc. max = = mc2 / . min = En / = = (Ze2)2m /(2n2 3), n = 1, 2, 3, ... ­ .
2 2 2n 2 ( r ) = -- ------ ln ------------- . 2 mc ( Z) 2

(18)

, , r
vac

= [ ( r ) ]

2

1/2

= / ( mc ) .

V(r) = = e(r) V + V
vac

= e(r + r ) = (19)

2 1 = e 1 + ( r ) + -- ( r ) + ... ( r ) , 2

, , r , ­ . (19) ( r ) = = ­ 4 ( r ) ( ( r ) ­ , :



( r ) dV = Z e ­

, Z = 1 ), : V
vac 2 4 2n = ­ -- e ------ ( r ) ln ------------- . 2 3 mc ( Z) 2

(20)

, ( r ) , E
vac

= V

vac

2n 4 mc 4 - = ----- -------- ( Z ) ln ------------- , 2 3 n3 ( Z)

2

2

(21)

( p ­ ). , E mc2 ( : mc2 E < ), - mc2 ( : - < E - mc2), . 2.

..

89





. ( ) "" (. . 2). ("") + e, ­ p
mc2

mc

2

-mc

2

-mc

2

. 2. .

, , 2mc2. , . , . . , , , . , - , . , , , . , , . , . , -

E = p 2 c + m c . "" . (e+) . , (e+e-)- . ­ , . ­ , . , : , , . e+ (1) (e+e-), / E /(mc2). r = c = /(mc), = /(mc) 10-11 . , . mc2 r, [4].
2 e 0 E cr ------ = mc , mc

2

24

mc E cr = ---------- 3 10 e0

23

16

/.

(22)

- . . , 137 | e | (22). . ,

90

, 7, 5, 2001



Ze, , . n = 1 j = 1/2 E
1, 1 / 2

= mc

2

1 ­ ( Z) .
2

(23)

Z (23) 0 (Z 137), Z . Z 137 . Z (n, j) = (1, 1/2) , , 0, . Z, (Z = Zcr), - m ( ). 1S1/2 , , Zcr = 169. Z > Zcr , . ? 1S1/2 (K-) ­ , Z = Zcr . , ­ . , , ­ "", ( 1S1/2 ). "" , , "" . . , (-2e), . , , . e+ , Z 170, .

Z1 Z2 : Z1 + Z2 > Zcr , 238U. 10- 22­10- 21 . ZU = Z1 + Z2 = 184 > Zcr , 1S1/2 . e+, () 1979 . , . , . , , , . .
1. .. // . 1998. 5. . 77­82. 2. .., .. . .: , 1988. 239 . 3. .., .. . .: , 1966. 152 . 4. .., .., .. . .: , 1989. 723 .

.. ***
, - , . ­ , . 60 .

..

91