lecture 3

11

22

33

44

55

Dirac 1927: search for a wave equation, in which the time derivative appears only in the first order

( Klein- Gordon equation: second time derivate is needed ) 66

4

3

2

1

77

0)( mi

4

3

2

1

88

4

3

2

1

lesantipartic

99

1010

positronpositron

1111

Dirac Dirac equationequation

1212

1313

1414

1515

1616

1717

1818

1919

2020

. . Suppose that the proton is a Suppose that the proton is a collection of 3 quarks (zero binding collection of 3 quarks (zero binding

energy).energy).The proton mass is the sum of The proton mass is the sum of

the three quark masses:the three quark masses:

mass (quark ) = mass (quark ) = M(proton)/3 M(proton)/3

=>one obtains the correct =>one obtains the correct magnetic moment of the protonmagnetic moment of the proton

2121

2222

2323

2424

The vector current and the The vector current and the axial vector current can beaxial vector current can be

measured by the measured by the electromagnetic and by the electromagnetic and by the

weak interactions.weak interactions.

The tensor, the scalar and theThe tensor, the scalar and thepseudoscalar densities cannotpseudoscalar densities cannot

be measured. be measured. 2525

2626

2727

2828

18261826conversion conversion

of of magnetismmagnetism

intointo electricity electricity

2929

3030

Quantum physics

3131

3232

3333

3434

3535

miL

mDiL

FF

4

1

ieAD 3636

miL

3737

AAF

mDiL

FF

4

1

3838

Dirac equation with interaction of electron and photonMaxwell equation

e

fieldphotonA

mieAi

:

0)((

3939

4040

4141

4242

4343

4444

)()( )( xex xi

4545

4646

xAA

ex xie

)()(

gauge theory

Intrinsic connection between charged fields and space-time

4848

hce /22

Arnold Arnold Sommerfeld, Sommerfeld, 19161916

4949

137

12

ch

e

5050

fine-structure constant hce /22

=0.00729735253

5151

03599976137

1

.

5252

5353

5454

5555

eVm

mm

e

e

511.0)(

)( 0

refdn

dd

Kl renormalization of the electron mass kl12

5656

refdn

ddKl renormalization of the electric charge

kl12

5757

303.0)(

)( 0

e

ee

Quantum Field Theory:Quantum Field Theory:

Finestructure constant becomes function of Finestructure constant becomes function of energy or scale due to quantum energy or scale due to quantum fluctuations of electron-positron pairsfluctuations of electron-positron pairs

=> partial screening of bare charge of the => partial screening of bare charge of the electron at distances less than the electron at distances less than the compton wavelength of the electroncompton wavelength of the electron

5858

+

5959

3

2

( , ) ( )ln( / )

( ) ...12

r

de q e e

d q M

QED

ee

6060

+

6161

OPAL

ALEPHL3

DELPHI

6262

(200 )GeV

( ) 1/127.8ZM 6363

Non-Abelean Non-Abelean gauge gauge theoriestheories

6464

6565

Pauli did not publish Pauli did not publish hishis

theory, since he did theory, since he did notnot

know, how to know, how to introduceintroduce

the masses for the the masses for the gauge bosons. gauge bosons.

6666

6767

Yang and Mills did not Yang and Mills did not mentionmention

the letter of Pauli in theirthe letter of Pauli in theirpaper, published in Phys. paper, published in Phys.

Rev.Rev.They disregarded the They disregarded the

problemproblemhow to introduce the masseshow to introduce the masses

of the gauge bosons.of the gauge bosons.

( In QCD no masses are ( In QCD no masses are

needed.) needed.)

6868

6969

7070

7171

Abelean gauge theory ( e.g. QED):

The gauge boson interacts only with the fermions.

Non-Abelean gauge theory ( e.g. QCD):

The gauge bosons interact with the fermions and with the gauge bosons - (e.g. in QCD: gluon-gluon scattering ).

7272