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