ФИАН / Nefedyev_Ktp

dΩ = 2πd cos θ

|p| |p′|

E1 ≡ E E3 ≡ E′

dσ

=

Tif

2

p′

π

=

|Tif |2

.

dt

64π|2(I/|

p

)2

| p

|

p

p′

|

||

|

64πI2

|

|

| |

T (s, t, u)

2

1

dσ =

| if |

dt,

I =

p(s − (m1

+ m2)2)(s − (m1 − m2)2).

64πI2

2

dσ =

dw/

t

=

1

iTif 2πδ(E1 − E2)

2

V d3p2

=

|Tif |2

2πδ(E

E )

d3p2

,

j

j t

√2E1V √2E2V

(2π)3

2E1v1

1

−

2 (2π)32E2

j

j = v /V

v

d3p2

1

1

3

2

E1v1 = |p1|

E2

d

p2 = p2dp2dΩ = |p2|E2dE2dΩ

δ

dσ

=

|Tif |2

|p2|

,

dΩ

16π2 |p1|

E1 = E2

|p2| = |p1|

|Tif |2

dσ

=

.

dΩ

16π2

d3p1

d3p2

d3p3

a + b → 1 + 2 + 3

dτ3 = (2π)4δ(4) (p1 + p2 + p3 − p)

,

p = pa + pb.

(2π)32E1

(2π)32E2

(2π)32E3

dτ3

1 =

Z (2π)4δ(4)(p12 − p1 − p2)

d4p12

Z

δ(p122

− m122 )dm122 =

(2π)4

Z (2π)4δ(4)(p12 − p1 − p2)

d3p12

dm2

=

12

,

(2π)32E12

2π

1 = Pb |bihb|

ha|ττ†|ai = ha|τ|bihb|τ†|ai = τabτab = |τab|2,

b

b

b

X

X

X

X

|τab|2.

2Imτaa =

b

T

τ = T

(2π)4δ(4)(Pi − Pf )

.

q i(2Ei0V )

f (2Ef V )

Q

Q

(2π)4δ(4)(0)

V

t

τaa = Taa

= Taa

,

Qi(2Ei0V )

Qi(2Ei0V )

(2π)4δ(4)(0) = Z

d4xe|ipxp=0 = Z

d4x = V

t.

τ

2

=

T

2

[(2π)4δ(4)(Pa − Pb)]2

=

V

t|Tab|2

(2π)4δ(4)(P

P

).

ab|

ab|

Qi(2Ei0V ) Qf (2Ef V )

Qi(2Ei0V ) Qf (2Ef V )

a −

|

|

b

2ImTaa =

b

Tab 2

b

′ Z

dτb|Tab|2

,

f|(2E|f V )(2π)4δ(4)(Pa − Pb) =

X

X

b = b

′

Z

f

V d3pf

!

,

(2π)3

X X

Y

b

V

2ImTaa = 4 (p1p2)2

− m12m22

b

′

Z

dσab = 4

(p1p2)2

− m12m22

σtot,

q

X

q

a

Taa

q

= √

|p|,

(p1p2)2 − m12m22

s

s = (p1 + p2)2

p

ImTe(0) = 2√

|p|σtot.

s

Te(0)

f(0)

dσe

=

|Te|2

=

f

2.

dΩ

64π2s

|

|

√

Te = 8π

sf.

σtot .

× ln2 s,

A = τ/2

AA†

1

(A − A†).

=

2i

A

A = K(1 − iK)−1,

K

K† = K

1−iK

1+iK

K

1 ± iK

K

M

s

1/(s − M2 + i0)

2

s = p

A → B + C

A

B + C → B + C

B + C → A → B + C → . . . → A → B + C

K

K

1

G(s),

K =

= G(s)

M2 − s

A → B + C

A

G(s)

B+C)

≡ (A →

g

G2(s)

g2

(s) =

√

, G2(s) = √

k2l+1,

s

s

l

(BC)

S

l = 0

Anr

( Anr, Anr)

√

K

K

s

1/(s − M2 + i (s)√

)

1/(s − M2 + i0)

s

A

(BC)

Anr =

ε + i

, ε =

2(E0 − E)

,

ε2 + 1

1

2

1

( Anr)2 +

Anr −

=

,

2

4

(x, y) = ( Anr, Anr)

E

Anr

−∞

+∞

Anr

E = E0

B+C → B+C

n(s)√

s

Anaive =

1 +

2,

n =

Mn2 − s − i n(s)√

.

s

Anaive

K

1(s)√

2(s)√

K =

s

+

s

,

M12 − s

M22 − s

|M1 − M2| 1,2

BW1 · BW2 → 0

A → B1 + C1, A → B2 + C2, A → B3 + C3, . . .

K

N × N N

1

Gj (s),

Kij = Gi(s)

M2 − s

Gi(s)Gj(s)

1

Xi

Gi2(s).

Aij =

M2 − s − i (s)√

, (s) =

√

s

s

i

i

i(s)√

s

Aii =

M2 − s − i (s)√

,

s

i

(s) = Pi i(s)

S

0

S

l = 0

√

(E) = g˜ E,

k = √

µ

B C

2µE

g˜

A

1

√

.

E − E0 +

i

2

( 0

+ g˜ E)

E → 0

∂A/∂E = ∞

K

A =

k

,

K−1 − ik

k

K

ˆ

4π(Zα)

T0 = −eu¯(p2)Au(p1) = −

u¯(p2)γ0u(p1).

(p2 − p1)2

(p2 − p1)2

(p2 − p1)2 = 2p sin 2

2

,

θ

p ≡ |p1| = |p2| θ

p1

p2

p2

1 − v2 sin2

θ

,

Sp((ˆp1 + m)γ0(ˆp2 + m)γ0) =

8

v2

2

v = |p1|/E1 = |p2|/E2

=

2πZα

2 1 − v2 sin2

2θ .

T0

2

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