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\begin{document}

 {\bf [Contributed Entry in Progress]}

This is a contributed topic entry listing notations of fundamental quantities and \htmladdnormallink{observables}{http://planetphysics.org/encyclopedia/Observable.html} in physics, as well as a listing of related notations of mathematical \htmladdnormallink{concepts}{http://planetphysics.org/encyclopedia/PreciseIdea.html} employed in \htmladdnormallink{mathematical physics and physical mathematics}{http://planetphysics.org/encyclopedia/MathematicalPhysicsAndPhysicalMathematics.html}.
\subsection{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}

\begin{enumerate}
\item $m= \, Mass$
\item $n, \, or \, N = Number \, of \, Particles$ in a System
\item $\mathcal{R} = \, System\, of \, Reference$ or (Relative) Reference Frame
\item $ \vec{r}$ or ${\bf r}= \, position \, in \, space$ (relative to a system of reference $\mathcal{R}$ or coordinate system)
\item $\mathcal{S} = \, Physical \, Space$
\item $A = \, Surface \, Area$
\item $l = \, length$
\item $ d = r_2 - r_1=  \, the \, distance$ between two points of relative \htmladdnormallink{positions}{http://planetphysics.org/encyclopedia/Position.html} $\vec{r}_1$ and $\vec{r}_2$
\item $V = \, Volume$
\item $\rho = \, Density$
\item $\sigma = \, Density \, of \, States$ (for example in a solid)
\item $ \eta = \, Viscosity$ of a Fluid
\item $\sigma_S =\, Surface \, Tension$
\item $ t = \, Time$ (relative to a system of reference $\mathcal{R}$)
\item {\bf v} or $ \vec{v} = Velocity$ in Newtonian mechanics
\item ${\bf q} =\, Velocity$ observable or, respectively \htmladdnormallink{operator}{http://planetphysics.org/encyclopedia/Observable.html} in theoretical and quantum physics
\item $\vec{p}= \, Momentum$ in \htmladdnormallink{classical mechanics}{http://planetphysics.org/encyclopedia/ClassicalMechanics.html} and relativity theories.
\item ${\bf p} = \, Momentum \, Operator$ in quantum mechanics, \htmladdnormallink{QFT}{http://planetphysics.org/encyclopedia/HopfAlgebra3.html}, etc.
\item $\vec{J} = \, Total, \, Quantized \, Angular \, Momentum$
\item $ \vec{a} =\, acceleration$
\item $ \vec{g} =\, gravitational \, acceleration$
\item $\vec{F} = \, Force$
\item $\vec{F}_v = \, Vector \, Field$
\item $T_{ij}, \, T^{ij}, \, g_{\mu \nu}, \, etc.\, = \, Tensor$ quantities
\item $E = \, Energy$
\item $E_i = \mathbb{U} = Internal \, Energy$
\item $U= \, Potential\, Energy$
\item $E_K =\, Kinetic\, Energy$
\item $\mathcal(H) = \, Hamiltonian$ or \htmladdnormallink{Schr\"odinger operator}{http://planetphysics.org/encyclopedia/HamiltonianOperator.html} \item $\vec{E} = \, Electrical\, Field$
\item $\vec{\mu}_E = \, Electric \, Dipole$
\item $\vec{m}= \, Magnetic \, Dipole$
\item $\vec{H}= \, Magnetic \, Field$
\item $H= Hadron \, number$
\item $I_z = Isospin \, z-axis \, component$
\item $\F = \, Flavor \, Quantum \, numbers$
\item $C_h = Charm \, observable$
\item $S = \, Strangeness number$
\item $Y= B + S = \, Hypercharge$
\item $C_{ol} = Color \, observable$ (in \htmladdnormallink{QCD}{http://planetphysics.org/encyclopedia/Gluons.html})
\item $ u = \, up \, quark$
\item $\overline{u} =  up \, Anti-quark$
\item $ d= down \, quark$
\item $ s = strange \, quark$
\item $ c= \, charmed \, quark$
\item $ b= \, bottom \, quark$
\item $ t= \, top \, quark$
\item $J/psi$ Particle
\item $\vec{B}= \, Magnetic \, Inductance$
\item $B = \, Baryon \, number$
\item $\vec{M}= \, Magnetization$
\item $ \mathcal{I} = \, Spin$ and \emph{\htmladdnormallink{spin}{http://planetphysics.org/encyclopedia/QuarkAntiquarkPair.html} Operator}
\item $EMF = \, Electromagnetic Field$
\item $Q = \, Electrical \, Charge$
\item $P =\, Parity$
\item $\vec{P} = \, Electrical \, Polarization$
\item $V_E = \, Electrical \, Potential$
\item $I = \, Electrical \, current$
\item $ i = \, Current \,, Density$
\item $C = \, Capacitance$
\item $L = \, Inductance$
\item $\mathbb{I} = \, Impedance$
\item $ R = \, Electrical \, Resistance$
\item $\E \, or\, \mu = \, Electrochemical Potential$
\item $ a = \, activity$
\item $T = Temperature$
\item $\Delta H = \, Exchanged \, Heat$
\item $\L = \, Mechanical \, Work$
\item $S = \, Entropy$ (\htmladdnormallink{Thermodynamic}{http://planetphysics.org/encyclopedia/Thermodynamics.html} \htmladdnormallink{state function}{http://planetphysics.org/encyclopedia/Observable.html})
\item $\Delta G =\, Gibbs \, Free\, Energy\, change$
\item $\Delta \mathbb{H} = \, Helmholtz \, Free \, Energy \, change$
\item ${\sigma}_{ij} =\, Pauli \, matrices$
\item $CQG = Compact \, Quantum \, Groups$
\item $QG = \mathcal{G} = \, Quantum Groupoids$
\item $QCG = \,Quantum \, Compact\, Groupoids$
\item $ QFG = \, Quantum \, Fundamental \, Groupoid$
\item $ \A =\, Abelian \, category$
\item $ \mathcal{C} = \, Category$
\item $\bf{G} = \, Group$
\item $ \G = \, Groupoid$
\item $ {\bf G}_S = \, Symmetry \, Groups$
\item $ {\bf g} = Lie \, group$
\item $ \widetilde{\bf g} =\, Lie \, algebra$
\item $SU =\, Special \, Unitary \, Groups$
\item K
\item L

\end{enumerate}

\subsubsection{Fundamental Constants in Physics}

\begin{itemize}
\item $c = \, magnitude \, of \, the \, velocity \, of \, light$ in vacuum
\item ${\epsilon}_0 =\, dielectric\, constant$, or \emph{electrical permitivity} of vacuum
\item ${\mu}_0 =\, magnetic \, permitivity \, (or \, permeability)$ of vacuum
\item $h = \, Planck's$ constant
\item $k =\, Boltzmann$ constant
\item $n = \, Avogadro's \, number$
\item Electron \htmladdnormallink{mass}{http://planetphysics.org/encyclopedia/Mass.html} (at rest), $e$
\item Proton mass (at rest) $m_P$
\item \emph{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 $\frac{1}{137}$)
\item \htmladdnormallink{Neutrino}{http://planetphysics.org/encyclopedia/Neutrino.html} masses (at rest), $m_{\nu}$
\item Electron \htmladdnormallink{charge}{http://planetphysics.org/encyclopedia/Charge.html}, $m_e$
\item Electron Magnetic Moment, $\mu_e$
\item Proton Magnetic Moment, $\mu_p$
\item Neutron Magnetic Moment, $\mu_n$
\item Gyromagnetic Ratios of \htmladdnormallink{nucleons}{http://planetphysics.org/encyclopedia/QuarkAntiquarkPair.html} or Nuclei, $g_n$
\item Gyromagnetic Ratio of the Electron, $g_e$
\item Gyromagnetic Ratio of the \htmladdnormallink{Muon}{http://planetphysics.org/encyclopedia/MuonLepton.html}, $g_{\mu}$
\item $G = \, Universal\, Gravitational\, Constant$
\item $ \lambda = \, Cosmological\, Constant$ (introduced by \htmladdnormallink{Einstein}{http://planetphysics.org/encyclopedia/Einstein.html} in Relativity Theory)
\item C
\item D
\item E
\end{itemize}

\end{document}
