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RELATIVISTIC KINETICS
S. A. SMOLYA NSKY

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. The methods and problems of relativistic kinetic theory , which is implemented to describe the evolution of non-equilibrium systems under extreme conditions, are discussed. Some applications of this theory to nuclear physics of intermediate and high energies are presented. , , . .
1. , , . . , . . . , , , . , , . ( , , ..). , . , , . , . . .

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, , . , , , ­ . . 2. () . , , f ( x, p, t ) 6- , x p d xd p , ( [1]). :
3 3

pk p4 = = / c ( ­ ) 4- pµ, m " " [2], 2 = c2(m2c2 + p2) = ± c m c + p , 2mc2. f (±)(x, p) , . , , (+) f (+)(x, p). , . , ( ). f (x, p) ( , ). , (V ­ )
22 2 (±)

1 ---------------- d p f ( x, p ) = n ( x ) , 3 (2 )



1 --- d x f ( x, p ) = n ( p, ) , (1) V





d x d p f ( x, p, t ) = 1
3 3

( ). . , (, ..), , . , (, ). , . (xk, k = 1, 2, 3) ґ (x4 = ct, c ­ ) , 4- xµ (µ = 1, 2, 3, 4) . 3-

( ) xµ . (1) dx (dp) () . " ": d f ( x, p ) -------------------- = D ( x, p ) + S ( x, p ) + I ( x, p ) , d (2)

­ [3]. . , . , , , , .

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(2), I(x, p), [2]: [4], (, ) , . S (x, p), (). f (x, p) , (xµ, pµ), . , pµ , µ p '1 ( µ , p '1 ). (. 1, ). , pµ, µ µ ' p 1 p 1 ( , . 1, ). ,
µ µ µ p + p ' = p 1 + p '1 . µ

f (x, p) p
µ

1 p (x, p) p'
µ µ 1

f (x, p1)

p1µ ' 1 f (x, p1) '

f (x, p')

1

f (x, p) p
µ

f (x, p) p (x, p) p'
µ µ 1

p1µ ' f (x, p')

1

f (x, p')

. 1. () ( ) , () ( ) pµ. , . 1 f (x, p) ( () ())

(3)

: S ( x, p ) = ­ d p ' d p 1 d p '1 W ( x p, p '; p 1, p '1 ) в в { f ( x, p ) f ( x, p ' ) [ 1 - f ( x, p 1 ) ] [ 1 - f ( x, p '1 ) ] ­ + + ' ­ [ 1 - f ( x, p ) ] [ 1 - f ( x, p ' ) ] f ( x, p 1 ) f ( x, p 1 ) }. + + (4)

( f (x, p) 1) (4) , : S ( x, p ) = ­ d p 1 d ( , , ) { f ( x, p ) f ( x, p ' ) ­ ' ­ f ( x, p 1 ) f ( x, p 1 ) }. (5)





, ­ . (4) . 1 f (x, p) . - () , ; - () . , 1 f (x, p) ( ) ( ) . µ , W ( x p, p ', p 1, p '1 ) (3).

= ­ ' ­ , d(, , ) ­ , , d = sin d d, . . (5) . (1872) . , , , . (4) - (5). - . . - , ,

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s(x, ) = = ­ d p f ( x, p ) ln f ( x, p ) ( ), , ds ( x, ) -----------------d 0.



. .. " ", 1946 . .. , .. , . , . , .. , .. , ., . , . . , , . , . . , , . - . , . , , . , . , (, ), ( ). ( , , [2]) . , , , , . , .

. - , , . , (2) -. , , , , . , (. . 1). , I(x, p), , I(x, p) , , (1) . , . [1]. , , , ( ) ( ) . ( . [5].) , (4), . , . , . , , , . ,

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3. , . . Tc 200 c (4­5)0 , 0 1014 /3 ­ . T T , , , , .. , T T , - , , . (T T , ) (T T , ). , . , . . . - [6]. , - (, ) (, -) (). () (N) -: NN NN, NN NN, ..., N N . , . , 102­103 , . - : (5), . , , , . , ( 25%). . : , , , ( ) .. . . , , . . , . , . ( -). , , . , , S (x, p) = I(x, p) = 0. (2)

.. , , , , . . , , , . ., [1], . ( ) -

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. , . . - . , . , . . 2 40 400 /. (x, y) . , , , a + b + + , ­ . . 2 , . , , . - (- ) . , 2, . y, 20 T = 0 / 5,0 7,5 10,0 12,5 15,0

. , - , , T . , . , , . ­ . , , , . . , T T , , [2]. , . ( , ..). ( ) [2]. ,

0

­20 20 17,5 20,0 22,5 25,0 27,5 32,5

0

­20 ­20 0 20 ­20 0 20 ­20 0 20 ­20 0 20 ­20 0 20 ­20 0 20 x,

. 2. 40 + 40 400 /. = 0,005; 0,01; 0,03 - 3 0,03 - 3. " " ; ­ ( 10­13 ), ­

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( ) " " , . , I(x, p) (1). . , u, d s 52 , . 4. " !" ­ .. .. . , , . . , . .
1. .. : . . II // . 1997. 12. . 78­83. 2. .. // . 2001. . 7, 2. . 69­75. 3. Smolyansky S.A., Prozorkevich A.V., Maino G., Mashnik S.G. A Covariant Generalization of the Real-Time Green's Functions Method in the Theory of Kinetic Equations // Ann. Phys. 1999. Vol. 277. P. 193. 4. .. " ": // . 1997. 6. . 84­90. 5. .., .., .. // . . 1997. . 166, 7. . 795­ 800. 6. Mashnik S.G., Smolyansky S.A. The Cascade-Exciton Approch to Nuclear Reactions // Proc. Europ. Sci. Foundation Study Centre "Dynamics of Transport in Plasmas and Charged Beams" / Ed. by G. Maino, M. Ottaviani. Singapore: World Sci., 1996. P. 137­159.

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, - , , . . .. . ­ . 100 .

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