V.M. Shabaev
(MPI, Heidelberg, 2002)
Contents
1) Introduction
2) Quantization of the free electromagnetic field
a) Radiation field as a collection of harmonic oscillators
b) Quantization of the radiation field
c) Emission and absorption of photons by atoms
3) Bethe’s evaluation of the Lamb shift
a) Electron self energy in non-relativistic approximation
b) Mass renormalization
4) Quantization of the electron-positron field
5) QED of interacting fields
a) Interaction representation
b) S-matrix and Green’s functions
c) Feynman diagrams
d) Renormalization
Energy levels:
Wave functions:
Notations:
Hydrogen
0
n=2 
-13.6 eV
n=1 
,
where 
, 
.
Wave functions:
The binding energy:
Fine structure splitting in hydrogen:
 |
10.9 GHz
Lamb shift
The Lamb shift is caused by the interaction of the electron with the quantized electromagnetic field and with the negative-continuum Dirac sea.
Hydrogen
________________ 
/
/ 1057 MHz
_________ /_ _ _______________ 
________________ 
/
/
/
/ 8173 MHz
/
/
__________/
Hyperfine splitting
The hyperfine splitting is caused by the interaction of the electron with the magnetic field induced by a non-zero nuclear magnetic moment.
 |
Hydrogen
_________________ 
_________/
\ 1420 MHZ
\_________________ 
Hydrogen
_________________
\ 
Non-relativistic \ ____________ _
__________ F=2
theory
\ F=1
\
\ 
\ F=1
\
/ F=0
\ 
/ 
\_____________/ _
___________ F=1
F=0
Fine structure Lamb Hyperfine
splitting shift splitting
_________________
\
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