ΣΠΑΣΙΜΟ ΣΥΜΜΕΤΡΙΑΣ Garamond.pdf

7/29/2019 Garamond.pdf

1/20

TO SU(2)XU(1) .

SU(2)WXU(1)Y

MSc.

2011


2/20

TO SU(2)XU(1) .


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


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

,


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) :


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


7/20

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 .


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)


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


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)


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).


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 ).

:


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)

. (

).

:


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


15/20

TO SU(2)XU(1) .

Higgs (Higgs, Englert,

Brout) 3 .

Higgs ( Standard Model) .

Higgs .

, .

Higgs ().

Higgs . (

).

Higgs LHC

CERN ( 2011-

...).


16/20

TO SU(2)XU(1) .


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


18/20

TO SU(2)XU(1) .

= vector bosons

Higgs ?

= quarks


19/20

TO SU(2)XU(1) .


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.

ΣΠΑΣΙΜΟ ΣΥΜΜΕΤΡΙΑΣ Garamond.pdf

Documents

Transcript of ΣΠΑΣΙΜΟ ΣΥΜΜΕΤΡΙΑΣ Garamond.pdf