Table 1. Symbols of the physical quantities of the Unified Family
a) dynamical plane
Row | Column | Dimension | Symbol | Physical quantity |
---|---|---|---|---|
-3 |
1 |
vector |
G |
gravitational factor |
-2 |
0 |
scalar |
f^{2} |
frequency square |
-2 |
1 |
vector |
a |
acceleration |
-2 |
2 |
bivector |
c^{2} |
squared velocity of light |
-2 |
3 |
vector |
fF |
temporal change of force |
-2 |
4 |
scalar |
P |
power |
-1 |
0 |
bivector |
f |
frequency |
-1 |
1 |
vector |
c |
velocity of light |
-1 |
2 |
scalar |
Φ_{f} |
circulation (flux of frequency) |
-1 |
3 |
vector |
F |
force |
-1 |
4 |
bivector |
W |
energy |
0 |
-3 |
vector |
n |
spatial density |
0 |
-2 |
bivector |
∆ |
Laplace operator |
0 |
-1 |
vector |
k |
wave vector |
0 |
0 |
scalar |
1 |
universal unity |
0 |
1 |
vector |
r |
length |
0 |
2 |
bivector |
A |
area |
0 |
3 |
vector |
p |
momentum |
0 |
4 |
scalar |
J |
action |
1 |
-2 |
scalar |
σ |
electric conductivity |
1 |
-1 |
vector |
ρ_{m} |
mass density |
1 |
0 |
bivector |
t |
time |
1 |
1 |
vector |
km |
linear distribution of mass |
1 |
2 |
scalar |
m |
mass |
2 |
-2 |
bivector |
ε |
dielectric factor |
2 |
-1 |
vector |
εr |
dielectric length |
2 |
0 |
scalar |
Φ_{ε} |
optical area (flux of ε) |
Table 1. Symbols of the physical quantities of the Unified Family
b) electrodynamic plane
Row | Column | Dimension | Symbol | Physical quantity |
---|---|---|---|---|
-1 |
0 |
bivector |
Bf |
temporal change of magnetic induction |
-1 |
1 |
vector |
fH |
temporal change of magnetic field |
-1 |
2 |
scalar |
E |
electric field |
-1 |
3 |
vector |
U |
electric potential |
-1 |
4 |
bivector |
Φ_{E} |
flux of electric field |
0 |
-2 |
bivector |
B∆ |
planar distribution of magnetic induction |
0 |
-1 |
vector |
Bk |
linear distribution of magnetic induction |
0 |
0 |
scalar |
j |
(planar) current density |
0 |
1 |
vector |
H |
magnetic field |
0 |
2 |
bivector |
i |
electric current |
0 |
3 |
vector |
Φ_{H} |
flux of magnetic field |
0 |
4 |
scalar |
µ^{~} |
magnetic dipole moment |
1 |
-1 |
vector |
ρ_{q} |
electric charge density |
1 |
0 |
bivector |
D |
planar distribution of electric charge |
1 |
1 |
vector |
kq |
linear distribution of electric charge |
1 |
2 |
scalar |
q |
electric charge |
1 |
3 |
vector |
qr |
electric dipole moment |
Table 2. The frequently used physical quantities equivalent to one of the „basic“ quantities of the Unified Family (listed in Table 1)
(The equivalent quantities are sorted here alphabetically; d means the dynamical plane, e means the electrodynamical plane of the unified family)
Equivalent physical quantity |
Equivalent symbol | Corresponding „basic“ quantity | „Basic“ symbol | Plane |
---|---|---|---|---|
angular momentum |
J |
action |
J |
d |
diffusion coefficient |
D |
circulation |
Φ_{f} |
d |
elastic force coefficient |
k |
circulation |
Φ_{f} |
d |
magnetic induction |
B |
planar current density |
j |
e |
electric inductance |
L |
length |
r |
d |
electric resistance |
R |
light velocity |
c |
d |
electric resistivity |
ρ |
circulation |
Φ_{f} |
d |
electrical mobility |
µ_{n} |
planar distribution of electric charge |
D |
e |
energy density |
ρ_{W} |
light velocity |
c |
d |
frequency flux |
J/m |
circulation |
Φ_{f} |
d |
heat flow |
G |
squared light velocity |
c^{2} |
d |
length cube |
r^{3} |
momentum |
p |
d |
magnetic flux density |
B |
planar current density |
j |
e |
magnetic induction |
B |
planar current density |
j |
e |
nabla-minus operator |
▼ |
wave vector |
k |
d |
optical path |
n_{λ} |
time |
t |
d |
optical path square |
εr^{2} |
optical area |
Φ_{ε} |
d |
period |
T |
time |
t |
d |
planar density |
k^{2} |
Laplace operator |
∆ |
d |
pressure |
p |
light velocity |
c |
d |
quantum of rotation |
K |
circulation |
Φ_{f} |
d |
radiation intensity |
S |
squared light velocity |
c^{2} |
d |
reciprocal length |
1/r |
wave vector |
k |
d |
reciprocal velocity |
1/c |
mass density |
ρ_{m} |
d |
reciprocal volume |
1/V |
spatial density |
n |
d |
refraction index |
n |
mass density |
ρ_{m} |
d |
refraction index square |
n^{2} |
dielectric factor |
ε |
d |
rotation |
ω |
frequency |
f |
d |
second time derivative |
∂^{2}/∂t^{2} |
frequency square |
f^{2} |
d |
spatial density of current |
i/V |
linear distribution of magnetic induction |
Bk |
e |
temporal force density |
∂F/∂t |
temporal change of force |
fF |
d |
thermodynamical mobility |
B_{n} |
Laplace operator |
∆ |
d |
time derivative |
∂/∂t |
frequency |
f |
d |
time derivative of B |
∂B/∂t |
temporal change of magnetic induction |
Bf |
e |
time derivative of H |
∂H/∂t |
temporal change of magnetic field |
fH |
e |
time square |
t^{2} |
optical area |
Φ_{ε} |
d |
velocity |
v |
light velocity |
c |
d |
viscosity coefficient |
η |
length |
r |
d |
voltage |
U |
electric potential |
U |
e |
volume |
V |
momentum |
p |
d |
volume expansion |
∂V/∂t |
force |
F |
d |
vorticity |
Ω |
frequency |
f |
d |
wavelength |
λ |
length |
r |
d |
work |
W |
energy* |
W |
d |
(*) Note that we have to use (because of our unification) the equivalent symbol W for energy if we wish to use simultaneously the electric field E having no common equivalent symbol.
Folker Meissner
Christian Humburg
Martina Schoener