Charged particles in electromagnetic fields interact with electromagnetic fields
1. Charged particles interact with stationary electromagnetic fields:
The symmetric-broken energy arises because of the Taylor expansion. In the region around the center of the particle, the matter is not evenly distributed, and the speed of the light quantum goes from
.The vibration energy
.
We
often tend to take the average of
at some point.
，
is the total curvature at
point. Please see the article:《
In-depth analysis of the curvature of general relativity
——Metric transformation function(1)
》. For example, in the calculation of the vibration
frequency of a particle, Taylor expansion uses the average expansion of
.But consider the external effect of each
mass point of light quantum system, it is necessary to consider the normal
curvature of each normal transversal line passing through on the equipotential surface in
all directions. Each normal transversal line has a different direction,
different normal curvature. The radius of normal curvature constitutes a broken
equiprobability vector. At each normal transversal line of the equipotential
surface of particles passing through point , the metric transformation function is
。
is the normal curvature of the distribution
surface of the light quantum of the particle through the normal transversal
line at this point. 
.
The Taylor expansion
should actually be used when considering the external effect of each mass
point of light quantum.
For each mass point of the light
quantum, 
is a directional
broken value. That causes the light quantum of particle to vibrate form of a
symmetry broken energy. When considering the external interaction
of particles, the energy broken part should be taken into account. 
According to the paper:《Equiprobability vector and symmetry- broken》, The mean of the equal probability vector is 0, the
product of equal probability vector and the oriented vector has a mean of 0.
The symmetric part of the vibrational energy of the particle does not
contribute to the external field. Only the broken part of the vibrational
energy is involved in the external field.
There are four
dimensional electromagnetic fields in the stationary coordinate system
,
field potential is
. The center of the particle
is at the origin of the coordinate system
.
In a small volume element 
around a point 
in space, Forced vibration
is produced for the light quantum system of the particle
under the action of four- dimensional
vibration momentum
of electromagnetic field. According to the above
article，the vibration energy of the particle is
, its energy is
symmetric-broken.
Only the momentum and energy of the broken part of the particle can participate
in the interaction between the field and the particle. The broken energy of light quantum
system of the particle in a small volume element participating in the forced
vibration of the field
potential is 
.
The momentum and
energy of the forced vibration of the light quantum system of the particle
in a small volume element
should be proportional to the potential of the four-
dimensional external field. The four- dimensional momentum that forces
the light quantum system of particle to forced vibrate in a small volume
element is:
. The four dimensional momentum of the
forced vibration of the whole particle is:
.
In the process of integrating with the sphere function, use:
，
，and
，
. ( please see the
paper< Symmetric equations of the light quantum systems> )
Let’s say the state function of the particle in its free state is
,
（defined 
，
）.
The
particle is forced to vibrate in the field, so that
its four-dimensional vector potential is
, its state function is
. Make
, and make
.
. Then, the state function of the particle
in the field is 
. Substituting it into
the original free particle
field equation:
If the equation of the free particle is
, then the equation of the
particle in the
field is:
The resulting is 
。
If the equation of the free particle is 
，make
, then the equation of the particlein the field is:
。
Due to
,we can get:：
.
Substitute
into 
can get：
If the equation of the free particle is and . And now we have the field
equation for the particle is
and
.
Comparing the equation of the free particle with the equation of the
particle in the field, if we make 
and convert 
into be 
in the equation of a free particle. 
，
According to Lorentz conditions, we can assume that
, then 
。
.
The field equations of quantum mechanical particles are:
and 
.
Can now become: 
and 
through the above operations. These
formulas are in perfect agreement with their counterparts in classical quantum
field theory.
These conclusions are completely consistent with classical quantum mechanics and quantum field theory, but the derivation process is different: No quantum hypothesis is used, not to the particle as a whole to discuss, but deep into the particle, through the mechanical principle of the light quantum system to analysis. It shows that the interaction between particle and field is completely the result of the interaction between the light quantum system of the particle and the light quantum system of field.
2. The interaction between charged particles
Let ，
are charged particles.
The center of the particle is at the origin of the coordinate
system
. The center
of the particle is
at the origin of the coordinate system
. the distance between the centers of the
two particles is d . The charge of particle is 
, The charge of particle is
. 
is a point in a small volume element around particle . At point, the light quantum of the
particle is
forced to vibrate due to the presence of the charged particle, so the energy of light quantum
system of in increases by
.
As described above, 
should be proportional to the broken
vibration energy 
of
particle in. As described in the
article《Symmetric equations of the light quantum
systems》and in the previous article, 
. Add in the foregoing
paragraph:
，
，and
，
，
，
we can get 
.
should also be proportional to the
vibration frequency
of the charged particle’and 
.
This intermediate: 
. 内The increased
energy of the light quantum system of the particle in is:
.
is the distance between the centers
of two particles. Integration in spherical coordinates, the total energy added
by the light quantum system of particle is:
is namely 
，
is namely
.
Similarly, the total energy added by the
light quantum system of the particle is also 
。
The force between the particle and the particle is:
。
These conclusions are completely consistent with classical quantum mechanics and quantum field theory, but the derivation process is different. It shows that the interaction between two particles is completely the result of the interaction between the light quantum systems of the two particles.
3. Lorentz force on charged particles in an electromagnetic field:
There is magnetic
induction intensity
in a stationary system
, let the center of the particleis at the origin of the coordinate system
. The particleand the coordinate
system are moving
uniformly with velocity 
relative to the coordinate system . In a small volume
element 
around a
point, the light
quantum system of the particle also has velocity relative to the coordinate system , thus it has
vibrational energy
.
At the same time, there is magnetic induction intensity in the stationary system, the magnetic induction intensity is the rotation of the
vibrational momentum of the light quantum system. Because of there is the
strength of magnetic induction observed from the stationary system. The light quantum of
particle
in has a rotational motion about at an angular velocity
. Rotational motion is motion
of following,
and velocity of following is:
, and acceleration of following is:
.
In the derivation of this formula, angular
velocity should be
proportional to the intensity of magnetic
induction, 
. is approximated as a constant vector,
should also be
approximated as a constant vector.
The force 
caused by the motion
of following of light quantum system in small volume element should be proportional to the acceleration
of following 
, it
should also be proportional to the energy of the broken part of the particle in. The energy of the broken part
of the particle is .
( See above ). Angular
velocity should be
proportional to the intensity of magnetic induction, 
. The force on the light quantum system of
the particle in
a small volume element is:.
（Please see the article: 《 Symmetric equations of the light quantum systems 》）
is the current density.
，，，
, etc. these are used in the integral of
the sphere function.
The particle is
also subjected to Coulomb forces
.
The
Lorentz force on a particle in an electromagnetic field is 
.
These are also full analyzed by the mechanics principles of the light quantum system.
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