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}


 * 1) $$m= \, Mass$$
 * $$n, \, or \, N = Number \, of \, Particles$$ 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)
 * 1) $$\mathcal{S} = \, Physical \, Space$$
 * 2) $$A = \, Surface \, Area$$
 * 3) $$l = \, length$$
 * 4) $$ d = r_2 - r_1= \, the \, distance$$ between two points of relative positions $$\vec{r}_1$$ and $$\vec{r}_2$$
 * 5) $$V = \, Volume$$
 * 6) $$\rho = \, Density$$
 * 7) $$\sigma = \, Density \, of \, States$$ (for example in a solid)
 * 8) $$ \eta = \, Viscosity$$ of a Fluid
 * 9) $$\sigma_S =\, Surface \, Tension$$
 * 10) $$ t = \, Time$$ (relative to a system of reference $$\mathcal{R}$$)
 * 11) {\mathbf v} or $$ \vec{v} = Velocity$$ in Newtonian mechanics #$${\mathbf q} =\, Velocity$$ observable or, respectively operator in theoretical and quantum physics
 * 12) $$\vec{p}= \, Momentum$$ in classical mechanics and relativity theories.
 * 13) $${\mathbf p} = \, Momentum \, Operator$$ in quantum mechanics, QFT, etc.
 * 14) $$\vec{J} = \, Total, \, Quantized \, Angular \, Momentum$$
 * 15) $$ \vec{a} =\, acceleration$$
 * 16) $$ \vec{g} =\, gravitational \, acceleration$$
 * 17) $$\vec{F} = \, Force$$
 * 18) $$\vec{F}_v = \, Vector \, Field$$
 * 19) $$Q = \, Electrical \, Charge$$
 * 20) $$T_{ij}, \, T^{ij}, \, g_{\mu \nu}, \, etc.\, = \, Tensor$$ quantities
 * 21) $$g_{\mu \nu} = \, Riemannian \, metric \, tensor$$ in general relativity #$$E = \, Energy$$ (term coined by Thomas Young in 1807)
 * 22) $$E_i = \mathbb{U} = Internal \, Energy$$
 * 23) $$U= \, Potential\, Energy$$
 * 24) $$E_K =\, Kinetic\, Energy$$
 * 25) $$\mathcal(H) = \, Hamiltonian \, operator$$ or Schr\"odinger operator #$$\vec{E} = \, Electrical\, Field$$
 * 26) $$\vec{\mu}_E = \, Electric \, Dipole$$
 * 27) $$\vec{m}= \, Magnetic \, Dipole$$
 * 28) $$\vec{H}= \, Magnetic \, Field$$
 * 29) $$H= Hadron \, number$$
 * 30) $$I_z = Isospin \, z-axis \, component$$
 * 31) $$\F = \, Flavor \, Quantum \, numbers$$
 * 32) $$C_h = Charm \, observable$$
 * 33) $$S = \, Strangeness \, number$$
 * 34) $$Y= B + S = \, Hypercharge$$
 * 35) $$C_{ol} = Color \, observable$$ (in QCD)
 * 36) $$ u = \, up \, quark$$
 * 37) $$\overline{u} = up \, Anti-quark$$
 * 38) $$ d= down \, quark$$
 * 39) $$ s = strange \, quark$$
 * 40) $$ c= \, charmed \, quark$$
 * 41) $$ b= \, bottom \, quark$$
 * 42) $$ t= \, top \, quark$$
 * 43) $$J/psi$$ particle #$$\vec{B}= \, Magnetic \, Inductance$$
 * 44) $$B = \, Baryon \, number$$
 * 45) $$\vec{M}= \, Magnetization$$
 * 46) $$ \mathcal{I} = \, Spin$$ and \htmladdnormallink{spin {http://planetphysics.us/encyclopedia/QuarkAntiquarkPair.html} Operator}
 * 47) $$EMF = \, Electromagnetic Field$$
 * 48) $$\mu = \, Magnetic \, Permeability$$
 * 49) $$\chi = \, Magnetic \, Susceptibility$$
 * 50) $$P =\, Parity$$
 * 51) $$\vec{P} = \, Electrical \, Polarization$$
 * 52) $$V_E = \, Electrical \, Potential$$
 * 53) $$I = \, Electrical \, current$$
 * 54) $$ i = \, Current \,, Density$$
 * 55) $$C = \, Capacitance$$
 * 56) $$L = \, Inductance$$
 * 57) $$\mathbb{I} = \, Impedance$$
 * 58) $$ R = \, Electrical \, Resistance$$
 * 59) $$\E \, or\, \mu = \, Electrochemical Potential$$
 * 60) $$ a = \, activity$$
 * 61) $$T = Temperature$$
 * 62) $$\Delta H = \, Exchanged \, Heat$$
 * 63) $$\L = \, Mechanical \, Work$$
 * 64) $$S = \, Entropy$$ (Thermodynamic state function)
 * 65) $$\Delta G =\, Gibbs \, Free\, Energy\, change$$
 * 66) $$\Delta \mathbb{H} = \, Helmholtz \, Free \, Energy \, change$$
 * 67) $${\sigma}_{ij} =\, Pauli \, matrices$$
 * 68) $$CQG = Compact \, Quantum \, Groups$$
 * 69) $$QG = \mathcal{G} = \, Quantum Groupoids$$
 * 70) $$QCG = \,Quantum \, Compact\, Groupoids$$
 * 71) $$ QFG = \, Quantum \, Fundamental \, Groupoid$$
 * 72) $$ \A =\, Abelian \, category$$
 * 73) $$ \mathcal{C} = \, Category$$
 * 74) $$\mathbf{G} = \, Group$$
 * 75) $$ \G = \, Groupoid$$
 * 76) $$ {\mathbf G}_S = \, Symmetry \, Groups$$
 * 77) $$ {\mathbf g} = Lie \, group$$
 * 78) $$ \widetilde{\mathbf g} =\, Lie \, algebra$$
 * 79) $$SU =\, Special \, Unitary \, Groups$$
 * 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