428
Σ ω
ω
ω
ω ω
ω
( ) =
( )
−
′
′
∞
′
∫
e
d
J
.
(21.23)
Here, the frequency ω b in Eq. (21.2) represents the cooling photonic frequency
mode in the PBG (0 < ω b < ω e ), calculated under the pole condition ω b − ω c − ∆(ω b ) = 0,
where
∆ ω
ω
ω
ω ω
( ) = ∫
( )
−
′
′
′
d
J
is a primary-value integral.
In details, it can be explained that PB is referred to as the Fock cooling determination n 0 , i.e., ρ(t 0 ) = |n 0 ⟩⟨n 0 |, which is obtained mathematically from the real-time
quantum field [51–53] by implementing Eq. (21.21) to consider the cooling- state
photon induction at time t:
ρ t
t n n
n
n
n
( ) =
( ) 〉〈
=
∞
( )
∑
0
0
0
0
,
(21.24)
n
n
n
n
n
k
n
t
v t t
v t t
t
0
0
0
1
1
1
0
( )
+
=
( ) =
( )
+ ( )
− ( )
×
,
,
,
Ω
min
n n
k
n
k
n
k v t t
{ }
∑
( )
( )
− ( )
0
1
1
,
t
t
Ω
Ω
, (21.25)
where
Ω t
u t t
v t t
( ) =
( )
+ ( )
,
,
0
2
1
. These results revealed that the Fock-state cooling photons
are indeed induced into dynamic states of earth plane n
n
t
0
( )
( ) of | n 0 ⟩. Figure 21.5
shows the plots of the proliferation of photon deliberation n
n
t
0
( )
( ) in the prime
state ∣n 0 = 5⟩ and in the steady-state limits n
n
t
0
( )
→ ∞
(
). Thus, the deliberation of
the generated cool-state photons shall eventually reach a nonequilibrium cooling
state which will cool the earth surface finally.
Heating Mechanism of Earth Surface
In the proposed theory, I have utilized the electromagnetic field of earth surface
formed by Higgs boson quantum dynamics. Here, the local U(1) gauge-variable
QED shall allow another mass in terms of gauge particles ∅
′
→ e
iα(x)
∅, which is the
cool-state photons that could be converted into thermal state photons in order to heat
the earth surface at a comfort level (Fig. 21.6). This mechanism can be tested by the
variable derivatives with the specific transformational rules for the scalar field, written by [55–57]
∂ →
= ∂ =
[
]
µ
µ
µ
µ
D
i eA
covariant derivatives ,
21 Climate Control
Σ ω
ω
ω
ω ω
ω
( ) =
( )
−
′
′
∞
′
∫
e
d
J
.
(21.23)
Here, the frequency ω b in Eq. (21.2) represents the cooling photonic frequency
mode in the PBG (0 < ω b < ω e ), calculated under the pole condition ω b − ω c − ∆(ω b ) = 0,
where
∆ ω
ω
ω
ω ω
( ) = ∫
( )
−
′
′
′
d
J
is a primary-value integral.
In details, it can be explained that PB is referred to as the Fock cooling determination n 0 , i.e., ρ(t 0 ) = |n 0 ⟩⟨n 0 |, which is obtained mathematically from the real-time
quantum field [51–53] by implementing Eq. (21.21) to consider the cooling- state
photon induction at time t:
ρ t
t n n
n
n
n
( ) =
( ) 〉〈
=
∞
( )
∑
0
0
0
0
,
(21.24)
n
n
n
n
n
k
n
t
v t t
v t t
t
0
0
0
1
1
1
0
( )
+
=
( ) =
( )
+ ( )
− ( )
×
,
,
,
Ω
min
n n
k
n
k
n
k v t t
{ }
∑
( )
( )
− ( )
0
1
1
,
t
t
Ω
Ω
, (21.25)
where
Ω t
u t t
v t t
( ) =
( )
+ ( )
,
,
0
2
1
. These results revealed that the Fock-state cooling photons
are indeed induced into dynamic states of earth plane n
n
t
0
( )
( ) of | n 0 ⟩. Figure 21.5
shows the plots of the proliferation of photon deliberation n
n
t
0
( )
( ) in the prime
state ∣n 0 = 5⟩ and in the steady-state limits n
n
t
0
( )
→ ∞
(
). Thus, the deliberation of
the generated cool-state photons shall eventually reach a nonequilibrium cooling
state which will cool the earth surface finally.
Heating Mechanism of Earth Surface
In the proposed theory, I have utilized the electromagnetic field of earth surface
formed by Higgs boson quantum dynamics. Here, the local U(1) gauge-variable
QED shall allow another mass in terms of gauge particles ∅
′
→ e
iα(x)
∅, which is the
cool-state photons that could be converted into thermal state photons in order to heat
the earth surface at a comfort level (Fig. 21.6). This mechanism can be tested by the
variable derivatives with the specific transformational rules for the scalar field, written by [55–57]
∂ →
= ∂ =
[
]
µ
µ
µ
µ
D
i eA
covariant derivatives ,
21 Climate Control