# PlanetPhysics/Fundamental Notations in Physics

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.

### Notations of Fundamental Physical Quantities, Observables and Related Mathematical Concepts

\subsubsection{A List of Notations for Fundamental Quantities, Observables Functions, Operators, Tensors and Matrices in Physics}
* $m=\,Mass$
* $n,\,or\,N=Number\,of\,Particles$ in a system #${\mathcal {R}}=\,System\,of\,Reference$ or (Relative) reference frame #${\vec {r}}$ or ${\mathbf {r} }=\,position\,in\,space$ (relative to a system of reference ${\mathcal {R}}$ or coordinate system)
* ${\mathcal {S}}=\,Physical\,Space$
* $A=\,Surface\,Area$
* $l=\,length$
* $d=r_{2}-r_{1}=\,the\,distance$ between two points of relative positions ${\vec {r}}_{1}$ and ${\vec {r}}_{2}$
* $V=\,Volume$
* $\rho =\,Density$
* $\sigma =\,Density\,of\,States$ (for example in a solid)
* $\eta =\,Viscosity$ of a Fluid
* $\sigma _{S}=\,Surface\,Tension$
* $t=\,Time$ (relative to a system of reference ${\mathcal {R}}$)
* {\mathbf v} or ${\vec {v}}=Velocity$ in Newtonian mechanics #${\mathbf {q} }=\,Velocity$ observable or, respectively operator in theoretical and quantum physics
* ${\vec {p}}=\,Momentum$ in classical mechanics and relativity theories.
* ${\mathbf {p} }=\,Momentum\,Operator$ in quantum mechanics, QFT, etc.
* ${\vec {J}}=\,Total,\,Quantized\,Angular\,Momentum$
* ${\vec {a}}=\,acceleration$
* ${\vec {g}}=\,gravitational\,acceleration$
* ${\vec {F}}=\,Force$
* ${\vec {F}}_{v}=\,Vector\,Field$
* $Q=\,Electrical\,Charge$
* $T_{ij},\,T^{ij},\,g_{\mu \nu },\,etc.\,=\,Tensor$ quantities
* $g_{\mu \nu }=\,Riemannian\,metric\,tensor$ in general relativity #$E=\,Energy$ (term coined by Thomas Young in 1807)
* $E_{i}=\mathbb {U} =Internal\,Energy$
* $U=\,Potential\,Energy$
* $E_{K}=\,Kinetic\,Energy$
* ${\mathcal {}H)=\,Hamiltonian\,operator$ or Schr\"odinger operator #${\vec {E}}=\,Electrical\,Field$
* ${\vec {\mu }}_{E}=\,Electric\,Dipole$
* ${\vec {m}}=\,Magnetic\,Dipole$
* ${\vec {H}}=\,Magnetic\,Field$
* $H=Hadron\,number$
* $I_{z}=Isospin\,z-axis\,component$
* Failed to parse (unknown function "\F"): {\displaystyle \F = \, Flavor \, Quantum \, numbers}
* $C_{h}=Charm\,observable$
* $S=\,Strangeness\,number$
* $Y=B+S=\,Hypercharge$
* $C_{ol}=Color\,observable$ (in QCD)
* $u=\,up\,quark$
* ${\overline {u}}=up\,Anti-quark$
* $d=down\,quark$
* $s=strange\,quark$
* $c=\,charmed\,quark$
* $b=\,bottom\,quark$
* $t=\,top\,quark$
* $J/psi$ particle #${\vec {B}}=\,Magnetic\,Inductance$
* $B=\,Baryon\,number$
* ${\vec {M}}=\,Magnetization$
* ${\mathcal {I}}=\,Spin$ and \htmladdnormallink{spin {http://planetphysics.us/encyclopedia/QuarkAntiquarkPair.html} Operator}
* $EMF=\,ElectromagneticField$
* $\mu =\,Magnetic\,Permeability$
* $\chi =\,Magnetic\,Susceptibility$
* $P=\,Parity$
* ${\vec {P}}=\,Electrical\,Polarization$
* $V_{E}=\,Electrical\,Potential$
* $I=\,Electrical\,current$
* $i=\,Current\,,Density$
* $C=\,Capacitance$
* $L=\,Inductance$
* $\mathbb {I} =\,Impedance$
* $R=\,Electrical\,Resistance$
* Failed to parse (unknown function "\E"): {\displaystyle \E \, or\, \mu = \, Electrochemical Potential}
* $a=\,activity$
* $T=Temperature$
* $\Delta H=\,Exchanged\,Heat$
* Failed to parse (unknown function "\L"): {\displaystyle \L = \, Mechanical \, Work}
* $S=\,Entropy$ (Thermodynamic state function)
* $\Delta G=\,Gibbs\,Free\,Energy\,change$
* $\Delta \mathbb {H} =\,Helmholtz\,Free\,Energy\,change$
* ${\sigma }_{ij}=\,Pauli\,matrices$
* $CQG=Compact\,Quantum\,Groups$
* $QG={\mathcal {G}}=\,QuantumGroupoids$
* $QCG=\,Quantum\,Compact\,Groupoids$
* $QFG=\,Quantum\,Fundamental\,Groupoid$
* Failed to parse (unknown function "\A"): {\displaystyle \A =\, Abelian \, category}
* ${\mathcal {C}}=\,Category$
* $\mathbf {G} =\,Group$
* Failed to parse (unknown function "\G"): {\displaystyle \G = \, Groupoid}
* ${\mathbf {G} }_{S}=\,Symmetry\,Groups$
* ${\mathbf {g} }=Lie\,group$
* ${\widetilde {\mathbf {g} }}=\,Lie\,algebra$
* $SU=\,Special\,Unitary\,Groups$
* K
* L

#### Fundamental Constants in Physics

* $c=\,magnitude\,of\,\,light\,velocity$ in vacuum
* ${\epsilon }_{0}=\,dielectric\,constant$, or electrical permitivity of vacuum
* ${\mu }_{0}=\,magnetic\,permitivity\,(or\,permeability)$ of vacuum
* $h=\,Planck's$ constant
* $k=\,Boltzmann$ constant
* $n=\,Avogadro's\,number$
* Electron mass (at rest), $e$
* Proton mass (at rest) $m_{P}$
* Fine-structure constant , $\alpha \,$, is the emf coupling constant (that characterizes the strength of the electromagnetic interaction); $\alpha \,=\ 7.297\,352\,570(5)\times 10^{-3}\ =\ {\frac {1}{137.035\,999\,070(98)}},$ (i.e., approximately ${\frac {1}{137}}$)
* Neutrino masses (at rest), $m_{\nu }$
* Electron charge, $m_{e}$
* Electron Magnetic Moment, $\mu _{e}$
* Proton Magnetic Moment, $\mu _{p}$
* neutron Magnetic Moment, $\mu _{n}$
* Gyromagnetic Ratios of nucleons or Nuclei, $\gamma _{n}$
* gyromagnetic ratio of the Electron, $\gamma _{e}$
* Gyromagnetic Ratio of the Muon, $\gamma _{\mu }$
* $G=\,Universal\,Gravitational\,Constant$
* $\lambda =\,Cosmological\,Constant$ (introduced by Einstein in Relativity Theory)
* C
* D
* E