429
A
A e
A
µ
µ
µ
µ
α
′
=
+ ∂
 
 
1
derivatives .
(21.26)
Here, the local U(1) gauge-invariant Lagrangian is considered as the perplex
scalar field that is expressed by
 = ( ) ∅
( ) −
− ∅
( )
D
D
F F
V
v
v
µ
µ
µ
µ
†
.
1
4
(21.27)
The term
1
4
F F
v
v
∝
∝ is the kinetic mechanism in the gauge field for considering thermal photons and V(∅) denotes the additional term written as
V(∅
∗
∅) = μ
2
(∅
∗
∅) + λ(∅
∗
∅)
2
.
As per the equation of the Lagrangian  , the perturbations of the quantum field
initiate the production of massive scalar particles ϕ 1 and ϕ 2 and a mass μ. Here,
μ
2
 < 0 shall be admitted as an infinite number of quanta in order to satisfy the equation φ φ
µ λ
1
2
2
2
2
2
+ = −
=
/
.
v In terms of the shifted fields η and ξ, the quantum field
is clarified as
φ
υ η
ξ
0
1
2
=
+
(
)+
 
 
i
, and the variable derivative of the Lagrangian
then confirms the following:
( ) ( ) ( )
(
) (
)
†
kin
*
Kinetic term:
,
D
D
ieA
i eA
m
m
m
m
m
m
h x
f
f
f
f
=
= ¶ +
¶ -
ℒ
(21.28)
Final term to the second order: V(η, ξ) = λ υ
2
η
2
. Thus, the full Lagrangian can be
written as
Fig. 21.6 The photon receptor where electron is heated on the surface of earth considering (a)
transforming of the curve step to reflection symmetry step for the determination of wavelengthinduced heating photon production. (b) Shows the functional coincidence rate of heating photon
production considering the detuning parameters of wavelength and absorption coefficient into the
band structure of earth plane [1, 24, 54]
Results and Discussion