Chemistry Reference
In-Depth Information
However, when employed for the Dirac equation terms, the field (10.22) modifies
the previous expressions (10.13a)-(10.13c) as follows
∂
t
R
ϕ
G
φ
G
ϕ
G
−
∂
t
S
1
√
2
1
√
2
R
i
h
e
c
∂
t
ℵ
∂
t
↔
G
=
+
+
(10.24a)
φ
G
√
2
∂
k
R
ϕ
G
ϕ
G
−
∂
k
S
1
√
2
R
i
1
e
c
∂
k
ℵ
∂
k
↔
0
=
+
+
(10.24b)
h
φ
G
φ
G
3
α
k
∂
k
↔
G
1
ˆ
k
=
φ
G
ϕ
G
h
k
∂
k
S
+
k
(
∂
k
R
)
−
φ
G
ϕ
G
1
√
2
√
2
R
i
1
e
c
∂
k
ℵ
=
σ
k
+
σ
k
(10.24c)
while producing the gauge spinorial Equation
⎡
Rϕ
G
∂
t
S
⎤
e
c
∂
t
ℵ
i
hϕ
G
∂
t
R
−
+
¯
⎣
⎦
hφ
G
∂
t
R
+
Rφ
G
∂
t
S
+
e
c
∂
t
ℵ
i
¯
⎡
Rcφ
G
k
∂
k
S
⎤
hcφ
G
k
(∂
k
R)
σ
k
+
mc
2
w
Rϕ
G
e
c
∂
k
ℵ
−
i
σ
k
−
ˆ
+
ˆ
+
¯
⎣
⎦
=
Rcϕ
G
k
∂
k
S
σ
k
−
mc
2
w
Rφ
G
hcϕ
G
k
(∂
k
R)
e
c
∂
k
ℵ
−
σ
k
+
ˆ
+
ˆ
+
i
¯
(10.25)
Now it is clear that since the imaginary part in (10.25) was not at all changed with
respect to Eq. (10.14) by the chemical field presence, the total charge conservation
(10.1) is naturally preserved; instead the real part is modified, respecting the case
(10.14), in the presence of the chemical field (by internal gauge symmetry). Nev-
ertheless, in order that chemical field rotation does not produce modification in the
total energy conservation, it imposes that the gauge spinorial system of the chemical
field must be as
⎧
⎨
φ
G
c
k
(
∂
k
ℵ
ϕ
G
∂
t
ℵ−
)
σ
k
=
ˆ
0
(10.26)
ϕ
G
c
k
(
∂
k
ℵ
⎩
σ
k
−
ˆ
φ
G
∂
t
ℵ=
)
0
According to the already custom procedure, for the system (10.26) having no trivial
gauge spinorial solution, the associated vanishing determinant is necessary, which
brings to light the chemical field Equation
c
2
k
(∂
k
ℵ
) σ
k
2
=
(∂
t
ℵ
)
2
(10.27a)
