Download INFORMATION ON MASTER`S THESIS 1. Full name: VU THI MINH

INFORMATION ON MASTER’S THESIS
1. Full name: VU THI MINH PHUONG
2. Sex: Female
3. Date of birth:
4. Place of birth: HAI DUONG
03/13/1979
5. Admission decision number:
Dated:
6. Changes in academic process: Change from optics to theoretical physics and
mathematical physics.
7. Official thesis title:
Anomalous magnetic moment of electrons and methods Pauli – Villars in quantum
field theory
8. Major: Theoretical physics and mathematical physics
9. Code: 60 44 01
10. Supervisors: Prof. Dr Nguyen Xuan Han - Faculty of Physics - University of
Natural Sciences - National University Hanoi.
11. Summary of the finding of the thesis:
Thesis: “Anomalous magnetic moment of electrons and methods Pauli –
Villars in quantum field theory” study the anomalous magnetic moment of the
electron in quantum field theory. The main complementary magnetic moment based
on perturbation theory via covariant Feynman diagrams. The divergent integrals are
solved by means of the Pauli-Villars - common methods and standards to preserve
immutability. The main results of the master thesis includes
1. Pauli equation and the magnetic moment of the electron.
1.1 Pauli equation
Starting from the Schrodinger equation with phenomenological thinking
we obtain the Pauli equation with terms of the magnetic moment of
electrons interacting with the external field:
i
  r , sz , t 
t
2
 1 

e0 
e

p

A
 e0  r   U  r   0 sH   r , sz , t 


c 
2m0c
 2m0 

(1.1)
here,   r  , A( r ) is the scalar potential of the electric field vector.
Equation (1.1) is the Pauli equation, by which we can explain Zeemann
effects.
1
1.2 Dirac equation for the electron in the external field in the
nonrelativistic limit v c I received Pauli equation by approximate
 
non-relativistic Dirac equation in external electromagnetic field in
approximate, v - is the velocity of the particle, and c is the speed of
light.
H nr

 H nr
t



2
3





1
e
e
v


0
   m0 c 2 
ˆ B   O  3  , 
 p  A   eA 
2m0 
c 
2m0c
c  



 0 

ˆ  

0 

i
(1.2)
If we were limited to positive, which means the first two components, then
this equation with precision m0 c 2 to coincide with the Pauli equation for spin-½
particles in external electromagnetic fields.
1.3 The main additional relativistic Pauli equation
The appointment followed the relativistic Pauli equation in higher-order
approximation is obtained by using transformation-Wouthuyen Fouldy
2. The Feynman diagrams for the contribution to the anomalous magnetic
moment of the electron
2.1 S-matrix
Matrix expression:
p2 S1 p1    p20  p10  R fi
(2.1)
R fi is determined by the following formula:
1/ 2
 m2 
R fi  2 e0 . 0 
 p10 p20 
u  p2    u  p1  Aext  p2  p1 
(2.2)
known as the scattering amplitude of electrons in a static external electric
field (Coulomb potential field) in the first approximation of perturbation theory
under electron.
2.2 Feynman diagrams for the contribution to the anomalous magnetic
moment
2
Figure 1
«True the top»   :
  p1 , p2        p1 , p2 
(2.3)
During   that summit «ceiling», and   p1 , p2  is determined by a set of schema
Figure 1
Electromagnetic form factor 2.3
Physical significance of the electromagnetic form factor, especially in nonrelativistic approximation
3. Additional key to the anomalous magnetic moment
3.1. Additional key for anomalous moment in a loop approximation
From the quadratic Feynman diagram in Figure 1 we have
 ie0  d 4q iD q   iS p  q  iS p  q 
( p1, p2 ) 
 F 2  
F 
F 1
4
 2  
2


(3.1)
Using the Pauli-Villars method we have isolated the ultraviolet divergent part and
the finite part of the additional terms for the magnetic moment. Part finite
expression: F2 (0) 
e2
8 2
(3.2)
3.2. Anomalous magnetic moment along with the additional quantum
Anomalous magnetic moment of the electron in quantum electrodynamics is
calculated to grade six, and weak interactions were included. The results we have:
3
1

  
 
g 1
 0,32848 
  (1,195  0,026)  
2
2
 2 
 
2
3
(3.3)
12. Practical applicability:
The content of the thesis research has high-value applications, it is: The
results obtained in the Master Thesis will be the basis for calculating the torque
from the study of elementary particles in quantum field theory more complicated.
.13. Further research directions:
The study calculated the magnetic moment of the particles in the theory underlying
the more complex
14. Thesis-related publications: None
Date: 12/12/2012
Signature:
Full name: Vu Thi Minh Phuong
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