Introduction to Quantum Electrodynamics

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     INTRODUCTION TO QUANTUM  

               ELECTRODYNAMICS

                            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

                     Introduction                                                         

                         Hydrogenlike atom

                     Non-relativistic theory

                                                                        *                

*  

*

Energy levels:   

Wave functions:  

Notations:   

                                 Hydrogen

          

          0                                                              

                                                                                   

                     n=2                                                               

                                                                                   

-13.6 eV       n=1                                                      

                                                                                  

                         Relativistic  theory

                             Dirac equation

,

where       ,         .

 Energy levels:
 

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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