Rotation transformation of Dirac equation under local condition

Abstract

The Dirac equation has the same form of rotation transformation and isospin transformation in space. The interaction behind the local rotation transformation of Dirac equation is constructed by using the method of Young Mills theory. The characteristics of particles correspond to interactions: mass corresponds to gravitational field, charge corresponds to electric field, isospin corresponds to isospin field, particle spin may correspond to an unknown interaction, and dark matter in cosmic space may be the manifestation of this interaction.

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1
Rotation transformation of Dirac equation under local condition
Bo Miao
zbl1905@126.com
摘 要
Abstract: The Dirac equation has the same form of rotation
transformation and isospin transformation in space. The interaction
behind the local rotation transformation of Dirac equation is
constructed by using the method of Young Mills theory. The
characteristics of particles correspond to interactions: mass
corresponds to gravitational field, charge corresponds to electric
field, isospin corresponds to isospin field, particle spin may
correspond to an unknown interaction, and dark matter in cosmic space
may be the manifestation of this interaction.
Keywords: Dirac equation, Yang Mills theory, space rotation
transformation, dark matter
1Global space rotation transformation of Dirac equation
The transformation of
ji xx ,
plane rotation is given in pages 34-35 of
reference [1]
 
 

iT






exp
2
1
exp
'
）
wherein

 
2
i
T
）
 

TifTT vv 
According to the requirements of the overall specification transformation,
it can be obtained that
 






TiJ 



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2
0


J
Where I is the Lagrange density of the field.
2 Local rotation transformation of Dirac equation
When
 
x
 

, it is necessary to construct the corresponding
gauge potential according to the method of Yang Mills theory.
 
xAD u




TigAA 
The gauge field strength corresponding to the gauge potential

ADADF v


TigFF 
 










AAfigAAF vv2

Action of gauge field
 

 dxFFTr uvuv
2
1
I
When
0I 

, we obtain
 
0, 

FAF v
Fermions and Lagrange Density of Gauge Fields
 
 
AigFFm uvuv  4
1
I
Reference:
[1]何宝鹏,熊钰庆.量子场论导论[M]. 华南理工大学出版社, 1990.