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(1)

"!$#% '&( *),+- +

.0/21432576982:;5=<>/ ?@1A8CBD:;14EF1A?2EFGA:F1A/HBF1E:F<I82:DJLKNMO<>EFPQ13SRT8C/U325LKIVIEWKIPQP(1DBF1PQ?2:YX

1A:F?ZK\[1I]2^KIE_1a`C1AP(?CJ=1D?b<>82EcJLKd32GA:F5e/HBFGV>EFK\BW5e<>/,3SRf82/%gb<>:F<I/%321ih25=VIV>:j1A/lkdJ=1?mBW<>/2:

τ

n

temps espace

τ p + 0 ,s 0

τ p,s h k

opJq:RTKIV>57Bj39RT82/,rtsOu2vqwxuZyzy|{}r~{-{€ƒ‚~y|uZ‚„]2…j1†325LKIVIEWKIPQP(1j1:;Bj82/210BWEWK\3282[‡X

BF5=<>/%:;[ˆh2GP(K\BF5=‰H821321JŠRTKIP(?CJ=5eBF823210321‹Z1AŒ/2P(KI/S]

Ž1:(:;ŒP4gb<>J=1A:}8CBF5=Je5=:FGA:N?@<>8CE}J=1A:(3C5e6@GEF1A/BW:}BpŒ?b1:,321 ?ZKIEYBW5=[A82J=1A:O:F[KIJLKI5eEF1A:‘

MO1AEFPQ5=<>/C:‘Cgb<>:;<>/2:"’>1[‡BW1A82EF:W“":;<>/B†3C<>/2/2GA:†3ZK\/2:"JLKd”ZV>8CEF1:F8257’\KI/BW1

n

boson scalaire fermion (spineur) photon, W, Z

bosons de jauge (vecteurs) gluon

…jhZK\‰8C1•?@<>5e/BD3214[AEF<>5e:F1AP(1A/HB–BWEWK\32825eB–82/2145e/BW1EFK\BW5e<>/

n

[IRf1:YB82/’>1AE;BW1a`@]ƒŽƒ1

—l<m32˜AJ=1™BWKI/23ZK\EF3l/21[<>/BW5e1/B0‰H8SRT8C/ /2<IP4g2EF1i”Z/C5321i’>1EYBW1a`|O’><I5=EF1i:;1[‡BW5=<I/ :;8257X

’\KI/BF1š“‡]^tKIE„1‡`m1PQ?2J=1\‘5=J2/9RT1a`C5e:;BF1†?ZK\:c321_’I1E;BF1‡`(?b<>82E„32G[AEF5eEF1"JLKi32576982:;5=<>/(…j<>PQ?mX

BF<>/

γe → γe

]x›D/[A<>P4g25e/ZK"KIJ=<IEF:S321A8m`i’I1E;BF1‡`

n

82/?2E;1PQ5=1AE328iBpŒm?b1

γe → e

K\8-BF1PQ?2:

t 1

1‡B082/ :;1[A<>/23

e → γe

KI8%BW1AP(?C:

t 2 ≥ t 1

]

œ~<>82:†J=1:†325LK\V>EWKIPQPQ1:_321•‹Z1‡Œm/CP}KI/ ?@1A8C’>1A/BKI5=/C:F5~:F1d[A<>/2:YBWEF8C5=EF11/UK\:F:F1APNX

gCJLKI/Bt[1:ž’I1EYBW1‡`4GJeGPQ1/BˆKI5eEF1A:t[A<>P(PQ1Ÿ321:ž?C5=˜[A1:ž3C1j?282 A Je1I]>ŽƒK–3C5e6@82:F5e<>/•…j<>PQ?mX

BF<>/-1:YBDKI5e/2:F5932G[AEF5eBF1i?ZKIE†k4325LK\V>EWKIPQPQ1:

(2)

voie s voie t

q 2 = (p 1 − p 3 ) 2 = t q 2 = (p 1 + p 2 ) 2 = s

p 1

p 2

p 3

p 4

p 1

p 4

p 3

p 2

"!4 *ƒ # (#‡ ~+l#-iž#

›D/UJe5=:;BF1d5e[5J RT1A/2:F1AP4g2Je1d321A:’I1EYBW1‡` KI8CBW<IEF5=:;G:D32KI/2:DJe1N— <32˜Je1N™BˆK\/23ZKIE;3U321

JLK•?2hŒ:F5=‰H821321:†?ZKIEYBW5=[A82J=1A:]2œ~<>8CBF15e/BW1EFKI[ABF5=<>/l328lP(<32˜AJ=1:;BWKI/23ZKIE;3 ?b18mB–32<I/2[

BWE;1d<>gmBW1/H8211/[A<>P4g25e/ZKI/B†?2J=82:;5=1A82EF:0321d[A1:–’I1EYBW1‡`@][ˆhZKI‰H821’>1EYBW1a`<>/ 32<>5eB

<>g2:F1AE;’I1E J RT1A/2:F1AP4g2Je1 3C1:lJ=<>5e:%321 [A<>/2:;1E;’\K\BF5=<>/ 32GA[<>82J=KI/B 3C1:l5=/’\KIEF5=KI/2[1A:-321

KI82V>1i328lPQ<m32˜AJ=1D1‡B0321JŠRf5=/’\KIEF5=KI/2[1–321Žƒ<IEF1/BF I‘•:WK ’><I5=E

n

…j<>/2:;1EY’IK BW5=<I/ 321J=K4‰82KI32EF5Xp5eP(?28CJ=:F5e<>/

…j<>/2:;1EY’IK BW5=<I/ 328l:F?C5=/

…j<>/2:;1EY’IK BW5=<I/ 321J=K4[ˆhZKIEFVI1GAJ=1A[ABWE;5=‰H821

…j<>/2:;1EY’IK BW5=<I/ 321UJ=K :WK ’>1A82E 3C1:-‰H8ZKIEH:l1AB-321A: Je1?CBF<>/2: O:WKI8CMd?@<I82E%J=1A:

[<I82EWKI/BF:†[ˆhZK\EFV>GA:"MK\5=g2Je1:ˆ“

…j<>/2:;1EY’IK BW5=<I/ 321J=K4[ˆhZKIEFVI13C1[A<>82Je182E

^t<>82E„:;5=PQ?2J=57”Z1EžJ RTGA[E;5eBW8CEF1_<>/Q/2<IBF1EWK:F8CEŸJe1:„325=KIV>EWK\P(PQ1:

q

?@<>8CEŸ8C/(‰H8ZKIE•‰H821JX [<>/2‰H821\‘

l

?@<I82Ej82/%Je1?CBF<>/%[ˆhZKIE;V>GD1‡B

ν l

?@<I82EjJe1–/21A8CBWE;5=/2<NKI:;:F<[5eGI]mŽƒ1A:"KI/BW5e?ZKIEYX BW5=[A82J=1A:DKI:;:F<[5eG1:–:F1E;<>/Bi/2<IBFG1A:

¯

q

‘

l +

1AB

ν ¯ l

] /C”Z/S‘93ZKI/2:DJe1d[KI:D3214J RT5e/BW1EFKI[ABF5=<>/

M KI5=g2Je1–<>/-325e:;BF5=/2V>8C1EWK4Je1:_‰H8ZKIEH:†321[ˆhZK\EFV>1

2 3



u

‘

c

1‡B

t

“j/2<IBFG:

q u

1‡B"J=1A:_‰82KIEH:

321[ˆhZKIEFVI1

1 3



d

‘

s

1‡B

b

“j/2<\BWG:

q d

]

(3)

{š{~w {šwby|u2vb‚šsƒ{

opJ/SRf1‡`m5e:;BW1‰H8SRf82/-BpŒm?b1321i’>1AE;BW1a`lGJe1[ABFEF<>P(KIV>/CGABW5e‰H821i[<>8C?2JLKI/B"Je1:*MO1E;P(5e<>/2:

[ˆh2KIEFV>GA:DKI8l?2h2<\BW<>/S]bŽ1?2h2<IBF<>/ /C1?b<>E;BF1dK\82[82/C1[ˆhZK\EFV>1\‘@5eJS1:YBD32<>/C[:FK(?2E;<>?2EF1

K\/HBF5=?ZK\E;BW5e[82Je1I]

q, l

q, l ¯ +

∝ √ α EM γ

{š{~wqw

Ž Rf5=/BW1AEWKI[‡BW5=<I/ MO<>E;BF14/21•[A<>/2[1AEF/21•‰H821•Je1:D‰H8ZK\EH:‰8C5?b<>E;BF1/B82/21•321A:DBWE;<>5=:

[ˆh2KIEFV>1A:(3C1 [A<>82J=1A82E  ?ZK\EQ[A<>/’>1A/HBF5=<>/

r

‘

v

1AB

b

“‡]„Ž1:(KI/BW5e‰H8ZKIEH:Q?@<IE;BW1A/B(8C/21 [ˆh2KIEFV>13SRTKI/BW5=[A<>82Je182EA]@ŽƒKNBWh2GA<>EF5e1d321 KI82V>1321dJ RT5e/BW1EFKI[ABF5=<>/-MO<>EYBW1EF1?b<>:;1d:F8CE–J=1

VIEF<>82?b1

SU (3)

1‡BM KI5eB5e/BW1EY’>1A/25=E321A:t[A<>82?2J=KIV>1A::F82?2?CJ=GPQ1/BWKI5=E;1:]š…j<>/BWEWK\5=EF1AP(1A/B K\8 ?Ch2<IBW<I/S‘_J=1UV>Je82<>/ 1A:;Bl?@<IE;BW1A82E-3SRf82/21 [ˆhZKIE;V>1 321 [<>82Je182E%1‡Bl3SRT8C/21 [ˆhZKIEFVI1

39RKI/BF5=[<I82J=1A82E]SopJ 1a`m5=:;BF1(1A/ BF<>8CBhH825eBVIJ=82<>/C:1‡BJŠRTKI/BW5=?2KIE;BF5=[8CJ=1d39RT82/ V>Je82<>/ 1:YB

8C/ K\8CBWE;1DV>J=8C<>/S]CopJ@1‡`m5=:YBW1KI5e/2:F5@321:_5e/BW1EFKI[ABF5=<>/C:*1/BWE;1iJ=1A:_V>J=82<I/2:j1A8m`HXpP

PQ1:‘

:FK ’><>5eEŸ3C1:Ÿ[<>82?CJLKIV>1A: BFEF<>5e: V>J=82<I/2: 1AB ‰82K\BWE;1†V>Je82<>/2:A]Ž1:Ÿ[<>8C?2JLKIVI1: i‰82K\BWE;1

VIJ=82<>/C:*MO<>/B"5=/BW1AE;’>1A/25=E"Je1i[ KIE;EFG321JLK4[A<>/2:;BWKI/BW1321[<>8C?2JLKIVI1I]

Ž1:_’I1E;BF1‡` 321JŠRf5=/BF1EWK\[ABW5e<>/}MO<>EYBW1i:;<>/B–32<I/2[

n

g c 1 c ¯ 2

∝ √ α s

q c 1

¯ q ¯ c 2

g c 1 ¯ c 3 ∝ α s

g g c 1 ¯ c 2 g

g c 2 c ¯ 3

∝ √ α s

g g

–KI/2:Q[1:N’>1AE;BF1‡`@‘cJe1:N5=/C325=[A1:

c i

3CG:F5eV>/21A/HB(321A:([A<>82J=1A82EF:QK ?2EF5e<>EF5j325e6@GE;1/BW1A:

n

J RT5e/BW1EFKI[ABF5=<>/,MO<IE;BW1iPQ<325e”Z1–JLK4[ˆhZKIE;V>1321[<>8CJ=18CE]

{š{~w uZs O{

Ž Rf5=/BW1AEWKI[‡BW5=<I/M KI5eg2J=1\‘ g2KI:FGA1_:F82EžJ RT5e/’IK\EF5LK\/2[1„321 K\82V>1

SU(2)

‘ MKI5eBKI?2?ZK\EWKeBWEF1 BFEF<>5e:cgb<>:;<>/2:j3C1 KI82VI1

n

321A8m`,gb<>:;<>/2:jGAJ=1A[ABWE;5=‰H821AP(1A/HBj[ˆhZKIE;V>G:

W +

1AB

W

‘mK\/HBF57X

(4)

?ZKIE;BF5=[A82J=1_J RT82/N3210JŠRTKI8CBFEF1_1‡Bc8C/}gb<>:F<>/Q/21A8CBWE;1

Z

‰H825q1:YBj:FK?2E;<>?2E;1†K\/HBF5=?ZK\E;BW5e[82Je1I]

Žƒ1A:c[A<>82EFKI/BW:j[ˆh2KIEFV>GA:iOG[ˆhZKI/CV>1–321

W ±

“ž:F<>/BjJ=1:Ÿ:F1A82J=:Ÿ:F8C:F[1A?CBW5eg2J=1A:j3210PQ<m3257”Z1E JLK :FK ’>18CE‘ :FKš’I<>5=E321}BFEWKI/2:YMO<>EFPQ1E82/ ‰H8ZKIE 321(BpŒm?b1

d

1/ ‰H8ZK\E|3C1}BpŒ?@1

u

<>8-82/ Je1?CBF<>/-[ˆhZKIE;V>G1A/ /C18CBFEF5=/C<Q1‡B05=/’>1AEF:F1AP(1A/B ]@…j1:0[ˆhZKI/2VI1PQ1/BW:0321:WK ’>1A82E

:F1NMO<>/B8C/25=‰H821AP(1A/HB -JŠRf5=/BWGAEF5e182ED39RT82/C1(P

PQ1•M KIP(5eJ=Je1I‘q:F<>57B

τ ↔ ν τ

‘

µ ↔ ν µ

‘

e ↔ ν e

‘

d ↔ u

‘

s ↔ c

‘

b ↔ t

]c…j<>PQP(1%3ZK\/2:(Je1%[ KI:QGJe1[‡BWEF<IP}KIVI/2GABF5=‰H821%1AB MO<>E;B‘J=1:„[A<>82EWK\/HBF:j/21A8CBWE;1:D gb<>:F<>/

Z

“ž/210P(<325e”21/BŸ?ZKI:ŸJLKi:WK ’>1A82E]mopJq1‡`m5=:YBW1032<>/B BWEF<I5=:d’I1E;BF1‡` 321-[A<>82?2J=KIV>1-KI8m`zMO1EFPQ5=<I/2:

n

Ž1:•MO1AEFPQ5=<>/2:•3C8 —l<m32˜AJ=1l™BWKI/23ZK\EF3

q ¯ d , l +

∝ √ α w

q ¯ u , ν ¯ l q, l ¯ + , ¯ ν l

W Z

W +

q, l , ν l

q d , l q u , ν l

GABˆK\/HBQP(KI:F:;5eMO:A‘<>/ P(<I/HBFEF1%‰H821-J=1A:NGABˆK BW:•?2E;<>?2EF1A:(3C1%JŠRf5=/BW1AEWKI[‡BW5=<I/zMO<>E;BF1%1ABQJ=1A:

GABˆK BW:"?2EF<I?2EF1A:†321?2E;<>?ZKIV>K\BW5e<>/  ?ZK\E;BW5e[82Je1:_Je5=g2E;1:ˆ“j/C1:;<>/B†?2KI:"J=1:"P PQ1:A]ZopJ1/

EFG:;82JeBF18C/ PQGJLK\/2V>1i321A:†:FKš’I182E;:D‰H825~[<>/23C825eB NJLKN?@<>:;:F5eg25=Je5eBWG–321BFEWKI/C:F5eBF5=<>/-?ZK\E

[<>82EFKI/B[ˆhZKIEFVIG(1A/HBFEF1(3218m` M K\P(5eJ=J=1A:D325769GAEF1/BF1:]t…j1A[5Ÿ/SRK 691A[ABW1Q‰H821QJ=1N:F1A[ABW1A82E

321–‰H8ZKIEH:‘CJe1:Ÿ/218mBWEF5e/2<>:cGABˆK\/HBj:WKI/C:jP(KI:F:;1–3ZKI/C:jJ=1–— <32˜Je1i™BWKI/23ZK\EF3S]mŽ RKIPQ?2Je57X

BW82321d3214[1A:DBWEFKI/2:F57BW5e<>/2:01:;BD[ KIEFKI[ABFGEF5e:FGA14?ZKIED8C/P}K BWEF5e[13214PQGJLK\/2V>182/25eBWKI5=E;1I‘

JLK4P(K\BWE;5=[1–321…*KIg2g25eg@<\X†<>g2KšŒ>KI:FhC57XY— KI: K*KN<>8-P(K\BWE;5=[1i…—

n

V CKM =

V ud V us V ub V cd V cs V cb V td V ts V tb

 =

0.974 0.226 0.004 0.226 0.973 0.042 0.009 0.041 0.999

^~<>82E†82/ ’>1AE;BF1‡`

W q u q d

JRKIPQ?2Je5eBW8C321i3214‹Z1‡Œm/CP}KI/lMKI5eB05e/HBF1EY’>1/C5=E–8C/ BW1AEFPQ1

∝ V q u q d

√ α w

]2Ž1A:*BW1E;P(1A:*325=KIV><>/ZK\8m`(321iJLKP}K\BFEF5e[1–:;<>/B"J=1A:*?2J=8C:*5=PQ?@<IE;BˆK\/HBF:c1‡B J=1:0[<I82?2JLK\V>1:"M KI5=gCJ=1:":;1MO<>/B†?2EF5e/2[5e?ZKIJ=1AP(1A/B QJŠRf5=/BWGAEF5e182E_3SRf82/21dP

P(1iM KIPQ5=JeJ=1

321‰82KIEH:]@Ž1[A<>82?2J=KIV>1i1A/HBFEF13218` M K\P(5eJ=J=101:YB–PQ<>5e/2:_?2EF<IgZKIg2Je1[A1‰H825ƒ?b1E;P(1‡B

3SRT1a`m?2J=5e‰8C1EŸJLKV>EWKI/C321†3C82EFGA1–3210’m5e1†3C1:j?2KIE;BF5=[8CJ=1:„[A<>/BW1/2KI/B*82/(‰82KIENGABFEWKI/CV>1



K 0

‘

K ±

‘

Λ

‘ƒ]]A]“†›i/ :WKI57BDKI8 <>82EF39RThH825~‰H8214J=1A:†/C18CBFEF5=/C<>:–:;<>/BDP(KI:F:;5eMO:01ABD‰H8SRf5=J 1‡`m5=:YBW1"GVK\J=1PQ1/B„82/C1†P(K\BWE;5=[A1_321"P(GAJLKI/2VI1_3ZKI/2:„J=1_:;1[‡BW18CEj321A:cJe1?CBF<>/2:‘HK\?2?@1AJ=GA1

P}K\BFEF5e[1i^Ÿ—–™ ^t<>/BW1A[<>EY’><\X — K K X–K KIVKjK XY™mK K\BˆK“a]

…j<IP(PQ13ZKI/2:†J=1[ KI:0321dJ RT5e/BW1EFKI[ABF5=<>/%MO<>EYBW1\‘b5eJƒ1‡`m5=:YBW1dGAVKIJe1PQ1/B0321:0BW1E;P(1A:

321j[A<>82?2J=KIV>1:~1/BFEF1jgb<>:;<>/2:3C1 KI82VI1DBWEF<I5=:~1ABt‰82K\BWE;1jgb<>:F<>/C:ˆ“~5e/2[Je8ZKI/BtJ=1Ÿ?2h2<IBF<>/

?2825=:;‰H821J=1:

W ±

?@<IE;BW1A/B†8C/21[ˆhZKIEFVI1GAJ=1A[ABWE;5=‰H821

n

(5)

Z/γ W

W +

W +

W W +

W

W W +

Z/γ Z/γ

{š{~w}r~{ sOvbv

Ž Rf8CBW5eJ=5=:FK\BW5e<>/N321iPQG[ K\/25=:;P(1†321†5eV>V>:c?@<>8CE*g2EF5e:F1AE*JLK:;ŒP(G‡BWE;5=1DGAJ=1[‡BWE;<IM KI5=gCJ=1

[A<>/2328C5eB iJŠRTKI?2?ZK\EF5eBF5=<>/d3SRT8C/(gb<>:F<I/Q:;[ KIJ=KI5=E;1*/21A8CBWE;1I‘HJ=1_gb<>:F<I/Q3C105=V>VI:‘>[A<>82?2JeG

BF<>8CBF1:_J=1A:_?ZKIEYBW5=[A82J=1A:*P(KI:F:;5e’>1A:

n

BW<I82:"J=1:cMO1EFPQ5=<I/2:4JŠRf1‡`m[A1?CBF5=<>/-321A:0/C18CBFEF5=/C<>:‘

Je1:(g@<>:;<>/2:(321 KI82VI1 321 JŠRf5=/BW1AEWKI[‡BW5=<I/ MKI5eg2J=1

W ±

1‡B

Z

1‡B,J=1lgb<>:F<>/ 321†5eV>V>:

Je8257X P

P(1dOBF1E;P(1A:_3SRK\8CBW<[<>8C?2JLKIVI1D3ZKI/2:_Je1i?@<\BW1/BF5=1JL“‡]mŽ RT5e/HBF1/2:;5eBFGi328-[<>82?CJLKIV>1

K\8m`}MO1AEFPQ5=<>/C:Ÿ1A:;B_?CEF<>?b<>E;BF5=<>/C/21JeJ=1 dJLKP}K\:F:F1†328}MO1AEFPQ5=<>/}KIJ=<>E;:c‰H821–J=10[<>82?CJLKIV>1

K\8m` g@<>:;<>/2:321 KI8CV>1}1A:;B4?CEF<>?b<>E;BF5=<>/C/21JŸKI8z[KIEFE;G}321(JLK-P}K\:F:F1(328zgb<>:F<I/S]Ž1A:

3C5e6@GEF1A/BW:_’>1AE;BW1a`l:F<>/B–KI5=/C:F5

n

q, l ¯ + q, l

∝ M 2

h h

∝ m h h

W + , Z W + , Z

W , Z W , Z

1‡B0?@<>8CE_J=1:"K\8CBW<[<>8C?2JLKIVI1:

n

∝ m h

h h

h h

h h

∝ λ

h

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Ici, on a besoin du mouvement pour définir le mouvement (ou encore : on a besoin du mouvement pour définir l’espace et le temps ; on a besoin de l’espace et du temps

Il n'y a donc aucune raison pour que mon futur soit parfaitement densifié et dans ce cas, un générateur quantique de nombres aléatoires aurait le pouvoir de réaliser au moment

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