Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://temporology.bio.msu.ru/RREPORTS/kurilin_teorii_polei_vremeni.pdf Äàòà èçìåíåíèÿ: Fri Feb 28 04:01:12 2014 Äàòà èíäåêñèðîâàíèÿ: Fri Feb 28 04:10:50 2014 Êîäèðîâêà:

Igor Kurilin

Digitally signed by Igor Kurilin DN: CN = Igor Kurilin, C = RU, O = FAZOTRON, OU = FAZOTRON Reason: I am the author of this document Location: Moscow, Russia Date: 2010.08.23 12:47:31 +04'00'

1

.A.



: << " " >>
" - " ( Web- " ": http://www.chronos.msu.ru/RREPORTS/kurilin_sviaznost.pdf) , , , . , . . , " " -. [1]. , (, (1.4.), [1]), , - , . , , , , , . , , , , , , . "" . [1] : 1). (. [1], , . ), .6),


2 , (. [1], (1.4.)). 2). ( [1] "" ), "" , [1] (. (1.14), (1.15)) " -". 3). 2 ([1], .9) [1] (2.4.D) ([1], .16). 4). (2.4.D). , [1] , [1].

I. "" .
, Uq ( "") "" {i}. , i Uq : (q) , i = 0,1,2,3 ­ " ". Uq , , Up ( q ­ ; , , ). {i} Q : en = n (: n - n). - en . , en. , , Uq 4 , Uq 4 . i Uq { }, 4. , [1] " ", ([1], (1.4), .7). ( 0 3 ) 4 Q . Uq 4- Q 4- ( Q) m (, m -


3 , : m=0), ( ) : (I.1) Xm(m) = Xm(m)(, ) , Xk(m)() = 0 , : k,m = 0,1,2,3 ; k m , ( : m=0 - ) . , , , (I.1). , , e0, . Uq . i(q) , 0 ( , ). Uq . , ( m=0), e0 , * "" : e (0) , =1,2,3. , * * * : (e0 , e (0)1 , e (0)2 , e (0)3). [1] " " ( m=0). (m=1,2,3), 1 , 2 3 . * * * * * * * * * : (e (1)0 , e1 , e (1)2 , e (1)3), (e (2)0 , e (2)1 , e2 , e (2)3), (e (3)0 , e (3)1 , e (3)2 , e3) ( 1, 2 3), " " (. [1], .12, 13). , "" (, " " m=0), , ( , e0)? . , (.. en, n=0,1,2,3 ) 4-, (.. ) "", . , "-" , ([1], . ), .13) "" , " ", en "". (.. "" ) . .1 , - , "" 3- ( 4- 4, ) , .1, " ". " " Uq "" ,


4 [1] ([1], . ), .8) ( ­ , . [1], (1.5.)) . , e0, " " ( .1 ) , " ". , .1 " 3-" :

/. 1/ , 3- , 3- e0 ( - , 0 ­ " ", " ", 1,2,3). , , . ( ), "" . , .


5 , "" . , ( ) , () . . , gij ([1], I, .11) ( S) (I.2):

(I.2)

g 'ij =

g' g' g' g'

00

g'

01

g'

02

g'

10 20 30

1 0 0

0 1 0

0 0 1
03

, : (g ij) = S ·(gij)·S

'

-1

(. 2), . ( ' ' ' e0) g 01 , g 02 , g 03 (I.2) .

/. 2/ , , (I.2).


6 , , ( , ), (I.3) : (I.3)

det( gij ) = g = 1

, :

x
j

, (: - x ), , , () . , {i}, gij, , (I.3).

(

)-

1 2



g

ij k

0

gij ( ) () Q, (I.3): (I.4.A)

(Dij) = Q-1·(gij)·Q , : (Dij) - :

(I.4.B)

( D ij ) =
i



0 0 0

0

0


0 0

1

0 0


0

2

3 0 0 0

,

: det( Dij ) = g = · · · = 1
0

1

2

3

: - (gij), . , Q , .
i

, . . : " () , ' (Dij) (g ij) (I.2)"? , (Dij) , : (I.4.)

(g ij) = H-1·(Dij)·H ,

'

(g ij) (I.2).

'

, , S = Q·H ' -1 : (g ij) = S ·(gij)·S .


7 H -, - D ( - ). , , ' (g ij) .
i

, -: (I.5.A)

det(g ij( )) = (1 - )2·[(1 - )·( g ij - ) - (g 01)2 - (g 02)2 - (g 03)2] = = ( 0 - )·( 1 - )·( 2 - )·( 3 - )

'

'

'

'

'

, (I.5.A) :

(I.5.B)

, ,

3 + g' 00 = 0 + µ 1 + 2(1 + g' 00 ) + g = 0 µ + , g (1 + g' 00 ) + 2g = 0 + 0 µ :
3

(I.4.): g = 1

µ = 1 + 2 +





= · + · + ·
1 2 1 3 2

3

; : · · · = 1 .
0

1

2

3

, (I.5.B) - . (I.5.B) µ . , , :

(I.6)

µ

= , 0 = 1 , g' 00 = µ - 2 , µ = 3 + (g' 01 ) 2 + ( g' 02 ) 2 + ( g' 03 )

2

, (I.6) (I.5.B) . , , , (I.5.). , , (I.6), : = 1.
0

, Q. q·Q (: q - ), :

(I.4.D)

(Dij) = Q-1·(gij) ·(q·Q) , : (Dij) - .
0 0

, q , : q = ( )-1, : = 1.


8 , g q:

det( Dij ) = g 1 ,
, , . , , , (I.2). "" . , , [1] (.13-15) (1.14) (1.15) , " " (.. , . .15) :



= 45 0 .

II .
[1] ([1], .9-10), (2.4.D) (. . (1.10.) [1], .16).

, X0 ( l), .. X ( = 1,2,3) l : X = X(0) = const. "" "" , () , , 3-. :

( II.1.A )

d 2x ds
2

i

=0,

: ds 0 4-. , { x } X0 ( , , [2]) , . , (. [2]) :

(

i

( II.1.B )

d dx
0

(

( x x

k

nl

)

= (

s

n

0

) ·(
l

( x x

k s

)

l

(II.1.B) l ,


9 X0. : ( (k x k 0 (x ) = dx l x 0 l , X0 l
( x - x ) :

0

( ( x k = (x k )

l

+

( 1 x k ( ) ·( x - x ) + ( 0 x l 2

s

l

) ·(

( x x

k

sl

) ·( x - x )·( x - x ) + ...
0 0

l (II.1.B). {

( x

i

} :

( II.1.C )

( d 2x ds
2

i

( d x k dx i [ ·] = ds x i ds
2i

=

dx i dx · ds i j ds x x

( 2x

k

·

j

(II.1.A): d x = 0. , X0 { x } , :

(

i

( II.1.D )

(

( 2x
i

k j

x x

)

l

=

( ) ·(
ij

s

( x x

k s

l

)

l

(II.1.) (II.1.D), , () 4- : dx0 0 , l :

( II.1.E )

(

( d 2x ds

k

2

)

l

=

( ) ·(
00

s

( x x

k s

l

)

l
s
00

(2.4.D) (. [1], .16). , l ( )
00



s

( - ), , , (II.1.E) :

l



( II.1.F )

( d 2x ds
2

i

=0


10 , (II.1.F) , , , :

( II.1.G )

d 2x ds

k

2

+



k ij

dx dx ds

i

j

ds

=0
s
00

, ( )

(2.4.D) ! (2.4.D), (. [1], .9) : 1) (1.9):

l



s
00






k

x

=

q g
00

g

0k

;




0

x

=q



g

00

2) (1.10.):

g

x

00 0

=

0

:

g

00

= g (x )
00



:

= 1,2,3

3) (1.10.):



( x , ) = q ( x , )
s

k

k

, (1.9), (1.10.) (1.10.) (2.4.D) ,
00

(II.1.F), (1.10.) (. [1], .9), 2:

d 2x d

i

2

C C 0 d (0) = - i0 = 0 : dx = - (0) = Const = C d d g g 00 00

III. -.
Rij ( ) " ". , " " (. [1], .26) , :


11

ij =

k

k + µ ij

g

ks



Tsij -


3

(Tijs - Tjis )

,

: µ , - .

(. , [3], .275-276) :

. - R

i qkl

, :

(III.1)

-R

i qkl

=

x

i ql k

-
i qlk



i qk l

x

+

i pk



p ql

- i
pl

p qk

:

(III.1.A)

R

i qkl

= -R +R
i klq

:

(III.1.B)

R

i qkl

+R

i lqk

0
, : R

, " " gij :

(III.1.C)

R

iqkl

= -R

qikl

iqkl

= g R
ip

p qkl
ij

, " " g :



(III.1.D)

R

iqkl

=R

kliq

,


i

s

:

(III.1.E)

( - ) = - R
i k l l k

s kl



s + ( s - s )
kl lk

i

x

s

(III.E) :

- s (R

is kj

+R

ksji

+R

p

js ik

)

p + ( s - s ) g + kj jk pi

x

s

+ ( s - s ) g
ji ij

pk

x

s

+ ( s - s ) g
ik ki pj

p

x

s

0

, (2.4.D), : , . s , :

(III.2.A)

R

iskj

+R

ks ji

+R

js ik

0


12 (2.4.D) " ", .. (III.1.C), (III.2.A) :

(III.2.B)

R

s
ikj

+R

s
kji

+R

s
jik

0

(III.2.B) s j :

(III.2.C)

R

ik

=R

ki

, (2.4.D), ­ " " . , 20 2010.

[1] .. . "
Web-

- ".
" ": 2010 ., http://www.chronos.msu.ru/RREPORTS/kurilin_sviaznost.pdf .

[2]

.. , ... " ".

, "", 1989 .

[3]
1986 .

.. , .. , .. . " :

". , "", - ,