This is a contributed topic entry (in progress) listing notations of fundamental quantities and observables in physics, as well as a listing of related notations of mathematical concepts employed in mathematical physics and physical mathematics .
\subsubsection{A List of Notations for Fundamental Quantities, Observables
Functions, Operators, Tensors and Matrices in Physics}
m
=
M
a
s
s
{\displaystyle m=\,Mass}
n
,
o
r
N
=
N
u
m
b
e
r
o
f
P
a
r
t
i
c
l
e
s
{\displaystyle n,\,or\,N=Number\,of\,Particles}
system #
R
=
S
y
s
t
e
m
o
f
R
e
f
e
r
e
n
c
e
{\displaystyle {\mathcal {R}}=\,System\,of\,Reference}
reference frame #
r
→
{\displaystyle {\vec {r}}}
r
=
p
o
s
i
t
i
o
n
i
n
s
p
a
c
e
{\displaystyle {\mathbf {r} }=\,position\,in\,space}
R
{\displaystyle {\mathcal {R}}}
S
=
P
h
y
s
i
c
a
l
S
p
a
c
e
{\displaystyle {\mathcal {S}}=\,Physical\,Space}
A
=
S
u
r
f
a
c
e
A
r
e
a
{\displaystyle A=\,Surface\,Area}
l
=
l
e
n
g
t
h
{\displaystyle l=\,length}
d
=
r
2
−
r
1
=
t
h
e
d
i
s
t
a
n
c
e
{\displaystyle d=r_{2}-r_{1}=\,the\,distance}
positions
r
→
1
{\displaystyle {\vec {r}}_{1}}
r
→
2
{\displaystyle {\vec {r}}_{2}}
V
=
V
o
l
u
m
e
{\displaystyle V=\,Volume}
ρ
=
D
e
n
s
i
t
y
{\displaystyle \rho =\,Density}
σ
=
D
e
n
s
i
t
y
o
f
S
t
a
t
e
s
{\displaystyle \sigma =\,Density\,of\,States}
solid )
η
=
V
i
s
c
o
s
i
t
y
{\displaystyle \eta =\,Viscosity}
σ
S
=
S
u
r
f
a
c
e
T
e
n
s
i
o
n
{\displaystyle \sigma _{S}=\,Surface\,Tension}
t
=
T
i
m
e
{\displaystyle t=\,Time}
R
{\displaystyle {\mathcal {R}}}
{\mathbf v} or
v
→
=
V
e
l
o
c
i
t
y
{\displaystyle {\vec {v}}=Velocity}
Newtonian mechanics #
q
=
V
e
l
o
c
i
t
y
{\displaystyle {\mathbf {q} }=\,Velocity}
operator in theoretical and quantum physics
p
→
=
M
o
m
e
n
t
u
m
{\displaystyle {\vec {p}}=\,Momentum}
classical mechanics and relativity theories.
p
=
M
o
m
e
n
t
u
m
O
p
e
r
a
t
o
r
{\displaystyle {\mathbf {p} }=\,Momentum\,Operator}
quantum mechanics , QFT , etc.
J
→
=
T
o
t
a
l
,
Q
u
a
n
t
i
z
e
d
A
n
g
u
l
a
r
M
o
m
e
n
t
u
m
{\displaystyle {\vec {J}}=\,Total,\,Quantized\,Angular\,Momentum}
a
→
=
a
c
c
e
l
e
r
a
t
i
o
n
{\displaystyle {\vec {a}}=\,acceleration}
g
→
=
g
r
a
v
i
t
a
t
i
o
n
a
l
a
c
c
e
l
e
r
a
t
i
o
n
{\displaystyle {\vec {g}}=\,gravitational\,acceleration}
F
→
=
F
o
r
c
e
{\displaystyle {\vec {F}}=\,Force}
F
→
v
=
V
e
c
t
o
r
F
i
e
l
d
{\displaystyle {\vec {F}}_{v}=\,Vector\,Field}
Q
=
E
l
e
c
t
r
i
c
a
l
C
h
a
r
g
e
{\displaystyle Q=\,Electrical\,Charge}
T
i
j
,
T
i
j
,
g
μ
ν
,
e
t
c
.
=
T
e
n
s
o
r
{\displaystyle T_{ij},\,T^{ij},\,g_{\mu \nu },\,etc.\,=\,Tensor}
g
μ
ν
=
R
i
e
m
a
n
n
i
a
n
m
e
t
r
i
c
t
e
n
s
o
r
{\displaystyle g_{\mu \nu }=\,Riemannian\,metric\,tensor}
general relativity #
E
=
E
n
e
r
g
y
{\displaystyle E=\,Energy}
E
i
=
U
=
I
n
t
e
r
n
a
l
E
n
e
r
g
y
{\displaystyle E_{i}=\mathbb {U} =Internal\,Energy}
U
=
P
o
t
e
n
t
i
a
l
E
n
e
r
g
y
{\displaystyle U=\,Potential\,Energy}
E
K
=
K
i
n
e
t
i
c
E
n
e
r
g
y
{\displaystyle E_{K}=\,Kinetic\,Energy}
(
H
)
=
H
a
m
i
l
t
o
n
i
a
n
o
p
e
r
a
t
o
r
{\displaystyle {\mathcal {(}}H)=\,Hamiltonian\,operator}
Schr\"odinger operator #
E
→
=
E
l
e
c
t
r
i
c
a
l
F
i
e
l
d
{\displaystyle {\vec {E}}=\,Electrical\,Field}
μ
→
E
=
E
l
e
c
t
r
i
c
D
i
p
o
l
e
{\displaystyle {\vec {\mu }}_{E}=\,Electric\,Dipole}
m
→
=
M
a
g
n
e
t
i
c
D
i
p
o
l
e
{\displaystyle {\vec {m}}=\,Magnetic\,Dipole}
H
→
=
M
a
g
n
e
t
i
c
F
i
e
l
d
{\displaystyle {\vec {H}}=\,Magnetic\,Field}
H
=
H
a
d
r
o
n
n
u
m
b
e
r
{\displaystyle H=Hadron\,number}
I
z
=
I
s
o
s
p
i
n
z
−
a
x
i
s
c
o
m
p
o
n
e
n
t
{\displaystyle I_{z}=Isospin\,z-axis\,component}
Failed to parse (unknown function "\F"): {\displaystyle \F = \, Flavor \, Quantum \, numbers}
C
h
=
C
h
a
r
m
o
b
s
e
r
v
a
b
l
e
{\displaystyle C_{h}=Charm\,observable}
S
=
S
t
r
a
n
g
e
n
e
s
s
n
u
m
b
e
r
{\displaystyle S=\,Strangeness\,number}
Y
=
B
+
S
=
H
y
p
e
r
c
h
a
r
g
e
{\displaystyle Y=B+S=\,Hypercharge}
C
o
l
=
C
o
l
o
r
o
b
s
e
r
v
a
b
l
e
{\displaystyle C_{ol}=Color\,observable}
QCD )
u
=
u
p
q
u
a
r
k
{\displaystyle u=\,up\,quark}
u
¯
=
u
p
A
n
t
i
−
q
u
a
r
k
{\displaystyle {\overline {u}}=up\,Anti-quark}
d
=
d
o
w
n
q
u
a
r
k
{\displaystyle d=down\,quark}
s
=
s
t
r
a
n
g
e
q
u
a
r
k
{\displaystyle s=strange\,quark}
c
=
c
h
a
r
m
e
d
q
u
a
r
k
{\displaystyle c=\,charmed\,quark}
b
=
b
o
t
t
o
m
q
u
a
r
k
{\displaystyle b=\,bottom\,quark}
t
=
t
o
p
q
u
a
r
k
{\displaystyle t=\,top\,quark}
J
/
p
s
i
{\displaystyle J/psi}
particle #
B
→
=
M
a
g
n
e
t
i
c
I
n
d
u
c
t
a
n
c
e
{\displaystyle {\vec {B}}=\,Magnetic\,Inductance}
B
=
B
a
r
y
o
n
n
u
m
b
e
r
{\displaystyle B=\,Baryon\,number}
M
→
=
M
a
g
n
e
t
i
z
a
t
i
o
n
{\displaystyle {\vec {M}}=\,Magnetization}
I
=
S
p
i
n
{\displaystyle {\mathcal {I}}=\,Spin}
\htmladdnormallink{spin {http://planetphysics.us/encyclopedia/QuarkAntiquarkPair.html} Operator}
E
M
F
=
E
l
e
c
t
r
o
m
a
g
n
e
t
i
c
F
i
e
l
d
{\displaystyle EMF=\,ElectromagneticField}
μ
=
M
a
g
n
e
t
i
c
P
e
r
m
e
a
b
i
l
i
t
y
{\displaystyle \mu =\,Magnetic\,Permeability}
χ
=
M
a
g
n
e
t
i
c
S
u
s
c
e
p
t
i
b
i
l
i
t
y
{\displaystyle \chi =\,Magnetic\,Susceptibility}
P
=
P
a
r
i
t
y
{\displaystyle P=\,Parity}
P
→
=
E
l
e
c
t
r
i
c
a
l
P
o
l
a
r
i
z
a
t
i
o
n
{\displaystyle {\vec {P}}=\,Electrical\,Polarization}
V
E
=
E
l
e
c
t
r
i
c
a
l
P
o
t
e
n
t
i
a
l
{\displaystyle V_{E}=\,Electrical\,Potential}
I
=
E
l
e
c
t
r
i
c
a
l
c
u
r
r
e
n
t
{\displaystyle I=\,Electrical\,current}
i
=
C
u
r
r
e
n
t
,
D
e
n
s
i
t
y
{\displaystyle i=\,Current\,,Density}
C
=
C
a
p
a
c
i
t
a
n
c
e
{\displaystyle C=\,Capacitance}
L
=
I
n
d
u
c
t
a
n
c
e
{\displaystyle L=\,Inductance}
I
=
I
m
p
e
d
a
n
c
e
{\displaystyle \mathbb {I} =\,Impedance}
R
=
E
l
e
c
t
r
i
c
a
l
R
e
s
i
s
t
a
n
c
e
{\displaystyle R=\,Electrical\,Resistance}
Failed to parse (unknown function "\E"): {\displaystyle \E \, or\, \mu = \, Electrochemical Potential}
a
=
a
c
t
i
v
i
t
y
{\displaystyle a=\,activity}
T
=
T
e
m
p
e
r
a
t
u
r
e
{\displaystyle T=Temperature}
Δ
H
=
E
x
c
h
a
n
g
e
d
H
e
a
t
{\displaystyle \Delta H=\,Exchanged\,Heat}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikiversity.org/v1/":): {\displaystyle \L = \, Mechanical \, Work}
S
=
E
n
t
r
o
p
y
{\displaystyle S=\,Entropy}
Thermodynamic state function )
Δ
G
=
G
i
b
b
s
F
r
e
e
E
n
e
r
g
y
c
h
a
n
g
e
{\displaystyle \Delta G=\,Gibbs\,Free\,Energy\,change}
Δ
H
=
H
e
l
m
h
o
l
t
z
F
r
e
e
E
n
e
r
g
y
c
h
a
n
g
e
{\displaystyle \Delta \mathbb {H} =\,Helmholtz\,Free\,Energy\,change}
σ
i
j
=
P
a
u
l
i
m
a
t
r
i
c
e
s
{\displaystyle {\sigma }_{ij}=\,Pauli\,matrices}
C
Q
G
=
C
o
m
p
a
c
t
Q
u
a
n
t
u
m
G
r
o
u
p
s
{\displaystyle CQG=Compact\,Quantum\,Groups}
Q
G
=
G
=
Q
u
a
n
t
u
m
G
r
o
u
p
o
i
d
s
{\displaystyle QG={\mathcal {G}}=\,QuantumGroupoids}
Q
C
G
=
Q
u
a
n
t
u
m
C
o
m
p
a
c
t
G
r
o
u
p
o
i
d
s
{\displaystyle QCG=\,Quantum\,Compact\,Groupoids}
Q
F
G
=
Q
u
a
n
t
u
m
F
u
n
d
a
m
e
n
t
a
l
G
r
o
u
p
o
i
d
{\displaystyle QFG=\,Quantum\,Fundamental\,Groupoid}
Failed to parse (unknown function "\A"): {\displaystyle \A =\, Abelian \, category}
C
=
C
a
t
e
g
o
r
y
{\displaystyle {\mathcal {C}}=\,Category}
G
=
G
r
o
u
p
{\displaystyle \mathbf {G} =\,Group}
Failed to parse (unknown function "\G"): {\displaystyle \G = \, Groupoid}
G
S
=
S
y
m
m
e
t
r
y
G
r
o
u
p
s
{\displaystyle {\mathbf {G} }_{S}=\,Symmetry\,Groups}
g
=
L
i
e
g
r
o
u
p
{\displaystyle {\mathbf {g} }=Lie\,group}
g
~
=
L
i
e
a
l
g
e
b
r
a
{\displaystyle {\widetilde {\mathbf {g} }}=\,Lie\,algebra}
S
U
=
S
p
e
c
i
a
l
U
n
i
t
a
r
y
G
r
o
u
p
s
{\displaystyle SU=\,Special\,Unitary\,Groups}
K
L
c
=
m
a
g
n
i
t
u
d
e
o
f
l
i
g
h
t
v
e
l
o
c
i
t
y
{\displaystyle c=\,magnitude\,of\,\,light\,velocity}
ϵ
0
=
d
i
e
l
e
c
t
r
i
c
c
o
n
s
t
a
n
t
{\displaystyle {\epsilon }_{0}=\,dielectric\,constant}
electrical permitivity of vacuum
μ
0
=
m
a
g
n
e
t
i
c
p
e
r
m
i
t
i
v
i
t
y
(
o
r
p
e
r
m
e
a
b
i
l
i
t
y
)
{\displaystyle {\mu }_{0}=\,magnetic\,permitivity\,(or\,permeability)}
h
=
P
l
a
n
c
k
′
s
{\displaystyle h=\,Planck's}
k
=
B
o
l
t
z
m
a
n
n
{\displaystyle k=\,Boltzmann}
n
=
A
v
o
g
a
d
r
o
′
s
n
u
m
b
e
r
{\displaystyle n=\,Avogadro's\,number}
Electron mass (at rest),
e
{\displaystyle e}
Proton mass (at rest)
m
P
{\displaystyle m_{P}}
Fine-structure constant ,
α
{\displaystyle \alpha \,}
α
=
7.297
352
570
(
5
)
×
10
−
3
=
1
137.035
999
070
(
98
)
,
{\displaystyle \alpha \,=\ 7.297\,352\,570(5)\times 10^{-3}\ =\ {\frac {1}{137.035\,999\,070(98)}},}
1
137
{\displaystyle {\frac {1}{137}}}
Neutrino masses (at rest),
m
ν
{\displaystyle m_{\nu }}
Electron charge ,
m
e
{\displaystyle m_{e}}
Electron Magnetic Moment,
μ
e
{\displaystyle \mu _{e}}
Proton Magnetic Moment,
μ
p
{\displaystyle \mu _{p}}
neutron Magnetic Moment,
μ
n
{\displaystyle \mu _{n}}
Gyromagnetic Ratios of nucleons or Nuclei,
γ
n
{\displaystyle \gamma _{n}}
gyromagnetic ratio of the Electron,
γ
e
{\displaystyle \gamma _{e}}
Gyromagnetic Ratio of the Muon ,
γ
μ
{\displaystyle \gamma _{\mu }}
G
=
U
n
i
v
e
r
s
a
l
G
r
a
v
i
t
a
t
i
o
n
a
l
C
o
n
s
t
a
n
t
{\displaystyle G=\,Universal\,Gravitational\,Constant}
λ
=
C
o
s
m
o
l
o
g
i
c
a
l
C
o
n
s
t
a
n
t
{\displaystyle \lambda =\,Cosmological\,Constant}
Einstein in Relativity Theory)C
D
E 
