FundamentalNotationsInPhysics 2009-02-16 12:54:18 2009-02-16 16:11:28 Topic overview of the Content of PlanetPhysics m v q p A B C E \E c light velocity in vacuum dielectric constance \I impedance inductance dielectric constant magnetic inductance magnetic field electric field vector field F G \Delta G Q I J K H L M S T l t r U V K \mu \nu \rho rho \psi \phi g g~ \lambda \eta mass reference frame space time length distance spacetime coordinate system reference frame position velocity momentum acceleration gravitational acceleration force charge potential energy electrochemical potential electrical fields magnetic fields emf electromagnetic field magnetic dipole Gibbs free energy speed of light heat exchanged mechanical work entropy Helmholtz free energy kinetic energy potential energy internal energy entropy energy-momentum tensor wave function eigenvalue eigenstate phase Hamiltonian operator cosmological constant Riemannian metric tensor % almost certainly you want these 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\newcommand{\TOP}{{\rm TOP}} \newcommand{\wti}{\widetilde} \newcommand{\what}{\widehat} \renewcommand{\a}{\alpha} \newcommand{\be}{\beta} \newcommand{\ga}{\gamma} \newcommand{\Ga}{\Gamma} \newcommand{\de}{\delta} \newcommand{\del}{\partial} \newcommand{\ka}{\kappa} \newcommand{\si}{\sigma} \newcommand{\ta}{\tau} \newcommand{\lra}{{\longrightarrow}} \newcommand{\ra}{{\rightarrow}} \newcommand{\rat}{{\rightarrowtail}} \newcommand{\oset}[1]{\overset {#1}{\ra}} \newcommand{\osetl}[1]{\overset {#1}{\lra}} \newcommand{\hr}{{\hookrightarrow}} {\bf [Contributed Entry in Progress]} This is a contributed topic entry 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. \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 positions $\vec{r}_1$ 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 operator in theoretical and quantum physics \item $\vec{p}= \, Momentum$ in classical mechanics and relativity theories. \item ${\bf p} = \, Momentum \, Operator$ in quantum mechanics, QFT, 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 Schr\"odinger operator \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 QCD) \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 $\vec{B}= \, Magnetic \, Inductance$ \item $B = \, Baryon \, number$ \item $\vec{M}= \, Magnetization$ \item $ \mathcal{I} = \, Spin$ and \emph{Spin 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 $S = \, Entropy$ (Thermodynamic State Function) \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 mass (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 Neutrino masses (at rest), $m_{\nu}$ \item Electron charge, $m_e$ \item Electron Magnetic Moment, $\mu_e$ \item Proton Magnetic Moment, $\mu_p$ \item Neutron Magnetic Moment, $\mu_n$ \item Gyromagnetic Ratios of Nucleons or Nuclei, $g_n$ \item Gyromagnetic Ratio of the Electron, $g_e$ \item $G = \, Universal\, Gravitational\, Constant$ \item $ \lambda = \, Cosmological\, Constant$ (introduced by Einstein in Relativity Theory) \item C \item D \item E \end{itemize}