424
D
i
iqA
qA
µ
µ
µ
µ
µ
µ
µ
µ
φ
φ φ
φ
φ
φ
σ
2
2
2
2
1
2
1
2
2
1
2
= ∂ + ∗ ∂ + ∗
= ∂
( ) + ∗ ∂
(
)
= ∂
r
r
r
r
r
Θ
Θ
( ( ) +
+
(
) ∗ ∂ +
(
)
2
2
2
2
v
qA
σ
µ
µ
Θ
.
(21.18)
The Lagrangian is then given by
 = ∂
( ) − ( )−
+
+
(
) ∗ ∂ +
(
)
1
2
1
4
2
2
2
2
µ
µ ν
µν
µ
µ
σ
ν σ
ν σ
F F
qA
Θ
.
(21.19)
To conduct the heat  heat
( ) into the magnetic field of earth surface into this
Lagrangian, I have expanded  heat as the energy series of the field into the earth and
then I have extracted the quadratic parts by defying the free particles:
 heat = ∂
( ) − ∗ −
+ ∗
+∂
(
)
1
2
2
1
4
2
2
2
2
2
2
µ
µ ν
µν
µ
µ
σ
λν σ
ν
F F
qA
Θ .
(21.20)
Thus, it will obviously initiate to form comfortable heating photons into the
quantum field of the earth plane, and the free particle (with Lagrangian  free ) shall
act as the real scalar particle to deliver heat on the earth surface considering intensity and wavelength (Fig. 21.4).
Results and Discussion
Cooling Mechanism of Earth Surface
To mathematically confirm the deliberation of cooling-state photons on the earth
surface plane, I have determined the dynamics of photonic proliferations by merging Eqs. (21.15) and (21.16). Due to the cool unit area requirement J(ω) and the
steady weak coupling limits, the earth surface plane absorbs the proliferated photons [8, 34]. Therefore, J(ω) of the quantum field areas is defined by the density of
states (DOS) of photon formed on the earth surface plane by the cool photon magnitudes V(ω) within the photon band (PB). Besides, photon delivery follows the
Weisskopf-Wigner theory [26, 35, 36]. Subsequently, all the proliferated HcPs shall
pass the dynamic-state mode (1D, 2D, and 3D) in the earth surface, as shown in
Table 21.1 [40–42].
In the 3D earth surface plane, Ω C is the standard frequency cutoff which can
avoid the bifurcation of the DOS.  Naturally, the 1D and 2D earth surface plane
conducts a sharp frequency cutoff at Ω d to avoid negative DOS. Here, Li 2 (x) and
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