ΣΠΑΣΙΜΟ ΣΥΜΜΕΤΡΙΑΣ Garamond.pdf
-
Upload
john-fiorentinos -
Category
Documents
-
view
222 -
download
0
Transcript of ΣΠΑΣΙΜΟ ΣΥΜΜΕΤΡΙΑΣ Garamond.pdf
-
7/29/2019 Garamond.pdf
1/20
TO SU(2)XU(1) .
SU(2)WXU(1)Y
MSc.
2011
-
7/29/2019 Garamond.pdf
2/20
TO SU(2)XU(1) .
-
7/29/2019 Garamond.pdf
3/20
TO SU(2)XU(1) .
,
(electroweak) (Standard
Model).
Lagrangian:
2 2 ( )( ) ( )
4
L
(1)
, SU(2) (SU(2) douplet) :
1 2
0
3 4
1 ( )
2
1 ( )
2
i
i
(2)
, 0
. ( (1)
SU(2) , U(1) : SU(2)
U(1) ).
+ 2 Lagrangian
2 . (
2 , + 2 - 2 , ( 2 0 ), free ( 0 )
Lagrangian (1) 4 ,
m).
(1) , ( 2 0 ),
:
2 2
min
2 ( )
2
(3)
http://en.wikipedia.org/wiki/Lagrangianhttp://en.wikipedia.org/wiki/Lagrangianhttp://en.wikipedia.org/wiki/Lagrangianhttp://en.wikipedia.org/wiki/Lagrangian -
7/29/2019 Garamond.pdf
4/20
TO SU(2)XU(1) .
U(1) , (3) vacuum
expectation value (vev) :
2
0 02
(4),
0 (ground state).
H Lagrangian (1):
i) glbal :
. exp( )
2
ai
(5)
ii) U(1) glbal :
exp( )ia (6)
SU(2) U(1) .
(local version), 3 SU(2) gauge ,
( ),iW x 1,2,3i U(1) ( )B x .
:
0
,
(covariant) :
.2
WD ig
,
-
7/29/2019 Garamond.pdf
5/20
TO SU(2)XU(1) .
U(1) :
2
B
ig
:
2 2 1 1 ( ) ( ) ( )4 4 4
GL D D F F G G
(7),
:
( . )2 2
W BD ig ig
(8)
F W W gW W (9)
G B B (10)
.
(
0, ,W W Z ) ( ).
()
vev .
Weinberg(1967) :
0
0 0
2
(11),
:2
2
(11) :
-
7/29/2019 Garamond.pdf
6/20
TO SU(2)XU(1) .
1( )
23
1( ) 0 0 0
2t (12),
U(1)
SU(2) isospin.
Steven Weinberg
:
1( )
2
3
1 0 0 ( 0 0 ) exp[ ( ) 0 0 0 0
2ia t (13),
1
(32
3)2
t
, (weak) isospin.
(12) ,
:
http://en.wikipedia.org/wiki/Steven_Weinberghttp://en.wikipedia.org/wiki/Steven_Weinberghttp://en.wikipedia.org/wiki/Steven_Weinberg -
7/29/2019 Garamond.pdf
7/20
TO SU(2)XU(1) .
0
exp( ( ). ) 1( ( ))2
2
i xH x
(14)
,
(14) (
):
0
1( ( ))
2H x
(15)
(15) Lagrangian
( ), :
2 21 2
Free
GL H H H
2 2
1 1 1 1 1 1
1 1 ( )( )
4 8W W W W g W W
2 2
2 2 2 2 2 2
1 1 ( )( )
4 8W W W W g W W
3 3 3 3
1 1 ( )( )
4 4W W W W G G
2
3 3
1 ( )( ).
8gW g B gW g B
(16),
( ),
: H H , 2 2H .
-
7/29/2019 Garamond.pdf
8/20
TO SU(2)XU(1) .
,
.
:
0
1( ( ))
2H x
, :
1 2
3
1 ( ) ( ( )) 2 2
( . )12 2
( ( )) ( ( ))2 22
ig W iW H xW B
ig ig ig ig
W H x B H x
, :
1 1 1 2 1 3 .W W W W
1 2 3
0 1 0 1 0
1 0 0 0 1
iW W W
i
3 1 2
1 2 3
W W iW
W iW W
, :
( . ) .2 2 2 2
W B ig ig ig ig W B
=
3 1 2
1 2 3
0
1 ( ( ))2
2
W W iW ig
H xW iW W
0
1( ( ))2
2
igB
H x
1 2
3
1 ( ) ( ( )
2 2
1 1 ( ( ) ( ( ))
2 22 2
igW iW H x
ig ig W H x B H x
(17)
-
7/29/2019 Garamond.pdf
9/20
TO SU(2)XU(1) .
(17) ,
, :
2 2 2 2 2
1 2 3 3
1 1 ( ) ( )( )
8 8g W W gW g B gW g B
,
(16).
(16) :
2Hm ( Higgs)
1W
2W
(1 2 3
, ,W W W) , :
1 2
2
W
gM M M
, 3W B .
:
2
3 3
1 ( )( )
8gW g B gW g B
,
3
gW g B .
:
3 cos sinW WZ W B
(18),
:
1
2 2 2
cos
( )
W
g
g g
1
2 2 2
sin
( )
W
g
g g
(19),
http://en.wikipedia.org/wiki/Higgs_bosonhttp://en.wikipedia.org/wiki/Higgs_bosonhttp://en.wikipedia.org/wiki/Higgs_bosonhttp://en.wikipedia.org/wiki/Higgs_bosonhttp://en.wikipedia.org/wiki/Higgs_boson -
7/29/2019 Garamond.pdf
10/20
TO SU(2)XU(1) .
:
3 sin cos
W WA W B (20)
(16), :
3 3 3 3
1 ( )( )
4W W W W
2
3 3
1 1 ( )( )
4 8G G gW g B gW g B
=
=1
( )( )4
Z Z Z Z
2 2 21 1 ( )8 4
g g Z Z F F
(21),
: F A A (22)
W , :
tanW
g
g
,
g g Weinberg (
Glashow)
, :
3
3
cos sin
sin cos
W W
W W
Z W B
A W B
(23)
-
7/29/2019 Garamond.pdf
11/20
TO SU(2)XU(1) .
, 3
W
B , ( )WR ,
:
3
( )
W
BAR
WZ
,
3
cos sin sin cos
W W
W W
BAWZ
(24)
(
).
(24), :
3
( ) W
B A
RW Z
3
cos sin
sin cos
W W
W W
B A
W Z
(25)
3
cos sin
sin cos
W W
W W
B A Z
W A Z
(26)
(26) (21),
(21).
-
7/29/2019 Garamond.pdf
12/20
TO SU(2)XU(1) .
:
2 2 21 1 1 ( )( ) ( ) ( )( )4 8 4
Z Z Z Z g g Z Z A A A A
:
i) A A
, 0A
M . A
, .
ii) Z :
1
2 2 21
( )2 cos
WZ
W
MM g g
(27),
( 0Z ( 0, ,W W Z ).
. (7) 12
:
3 Ws , 8 (=42) , 4
4 ( vector 2
, ).
:
3 :1 2
,W W Z , : 33=9 ,
A 2
H (1 ).
:
-
7/29/2019 Garamond.pdf
13/20
TO SU(2)XU(1) .
0
1( ( ))
2H x
,
Ws 0Z , :2
2 2
.[ ]i gM
M i
A ,
D(
A
Z
),
:
23 3 31 1
{ sin ( ) [ sin ( )] }2 cos 2 2
W W
W
igD ig A Z
(28)
, 31
0 0 (
(12))
A
,
0 0 0 .
3
1
( ).
D
:
sinW
e g (29)
(16)
. (
).
:
-
7/29/2019 Garamond.pdf
14/20
TO SU(2)XU(1) .
2 1
3
0
12
2
ii
,
t Hooft:
2 2 2
3
1,2
1 { ( ) ( ) ( ) }
2i W i Z
i
W M Z M A
(30)
:
2 2 1
2 2
(1 )[ ]( )i g M
M
(31)
( ).
( , (31)
, - 21
,
QED Lorentz).
WeinbergW :
cos WW
Z
M
M (32),
Q, .
-
Q=91,2GeV/c, Z
M -boson. :
2sin 0, 23W , : 28,7W
-
7/29/2019 Garamond.pdf
15/20
TO SU(2)XU(1) .
Higgs (Higgs, Englert,
Brout) 3 .
Higgs ( Standard Model) .
Higgs .
, .
Higgs ().
Higgs . (
).
Higgs LHC
CERN ( 2011-
...).
-
7/29/2019 Garamond.pdf
16/20
TO SU(2)XU(1) .
-
7/29/2019 Garamond.pdf
17/20
TO SU(2)XU(1) .
Glashow-Salam-Weinberg
:Sheldon Lee Glashow, USA,Abdus Salam, Pakistan,
and Steven Weinberg, USA, Nobel 1979
().
http://en.wikipedia.org/wiki/Sheldon_Lee_Glashowhttp://en.wikipedia.org/wiki/Sheldon_Lee_Glashowhttp://en.wikipedia.org/wiki/Sheldon_Lee_Glashowhttp://en.wikipedia.org/wiki/Abdus_Salamhttp://en.wikipedia.org/wiki/Abdus_Salamhttp://en.wikipedia.org/wiki/Steven_Weinberghttp://en.wikipedia.org/wiki/Steven_Weinberghttp://www.nobelprize.org/nobel_prizes/physics/laureates/1979/http://www.nobelprize.org/nobel_prizes/physics/laureates/1979/http://www.nobelprize.org/nobel_prizes/physics/laureates/1979/http://www.nobelprize.org/nobel_prizes/physics/laureates/1979/http://www.nobelprize.org/nobel_prizes/physics/laureates/1979/http://www.nobelprize.org/nobel_prizes/physics/laureates/1979/http://www.nobelprize.org/nobel_prizes/physics/laureates/1979/http://en.wikipedia.org/wiki/Steven_Weinberghttp://en.wikipedia.org/wiki/Abdus_Salamhttp://en.wikipedia.org/wiki/Sheldon_Lee_Glashow -
7/29/2019 Garamond.pdf
18/20
TO SU(2)XU(1) .
= vector bosons
Higgs ?
= quarks
-
7/29/2019 Garamond.pdf
19/20
TO SU(2)XU(1) .
-
7/29/2019 Garamond.pdf
20/20
TO SU(2)XU(1) .
1. Gauge Theories in Particle Physics, I J R Aitchison-A J G Hey, volume (II): QCD and theElectroweak Theory, Taylor & Francis 2004.
2.A Modern Introduction to Quantum Field Theory, Michele Maggiore, Oxford University Press
2005
3.An Introduction to Quantum Field Theory, M E Peskin-D V Schroeder,Reading MA: Addison
Wesley, 1995.
4. The Quantum Theory of Fields, volume (II) Modern Applications, Steven Weinberg, CambridgeUniversity Press, 1996.
5.Quantum Field Theory in a Nutshell,A.Zee, Princeton University Press, 2003
6. Field Quantization, W. Greiner-J. Reinhardt, Springer 1996.