# 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. $m=\,Mass$
2. $n,\,or\,N=Number\,of\,Particles$  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)
3. ${\mathcal {S}}=\,Physical\,Space$
4. $A=\,Surface\,Area$
5. $l=\,length$
6. $d=r_{2}-r_{1}=\,the\,distance$  between two points of relative positions ${\vec {r}}_{1}$  and ${\vec {r}}_{2}$
7. $V=\,Volume$
8. $\rho =\,Density$
9. $\sigma =\,Density\,of\,States$  (for example in a solid)
10. $\eta =\,Viscosity$  of a Fluid
11. $\sigma _{S}=\,Surface\,Tension$
12. $t=\,Time$  (relative to a system of reference ${\mathcal {R}}$ )
13. {\mathbf v} or ${\vec {v}}=Velocity$  in Newtonian mechanics #${\mathbf {q} }=\,Velocity$  observable or, respectively operator in theoretical and quantum physics
14. ${\vec {p}}=\,Momentum$  in classical mechanics and relativity theories.
15. ${\mathbf {p} }=\,Momentum\,Operator$  in quantum mechanics, QFT, etc.
16. ${\vec {J}}=\,Total,\,Quantized\,Angular\,Momentum$
17. ${\vec {a}}=\,acceleration$
18. ${\vec {g}}=\,gravitational\,acceleration$
19. ${\vec {F}}=\,Force$
20. ${\vec {F}}_{v}=\,Vector\,Field$
21. $Q=\,Electrical\,Charge$
22. $T_{ij},\,T^{ij},\,g_{\mu \nu },\,etc.\,=\,Tensor$  quantities
23. $g_{\mu \nu }=\,Riemannian\,metric\,tensor$  in general relativity #$E=\,Energy$  (term coined by Thomas Young in 1807)
24. $E_{i}=\mathbb {U} =Internal\,Energy$
25. $U=\,Potential\,Energy$
26. $E_{K}=\,Kinetic\,Energy$
27. ${\mathcal {(}}H)=\,Hamiltonian\,operator$  or Schr\"odinger operator #${\vec {E}}=\,Electrical\,Field$
28. ${\vec {\mu }}_{E}=\,Electric\,Dipole$
29. ${\vec {m}}=\,Magnetic\,Dipole$
30. ${\vec {H}}=\,Magnetic\,Field$
31. $H=Hadron\,number$
32. $I_{z}=Isospin\,z-axis\,component$
33. $\displaystyle \F = \, Flavor \, Quantum \, numbers$
34. $C_{h}=Charm\,observable$
35. $S=\,Strangeness\,number$
36. $Y=B+S=\,Hypercharge$
37. $C_{ol}=Color\,observable$  (in QCD)
38. $u=\,up\,quark$
39. ${\overline {u}}=up\,Anti-quark$
40. $d=down\,quark$
41. $s=strange\,quark$
42. $c=\,charmed\,quark$
43. $b=\,bottom\,quark$
44. $t=\,top\,quark$
45. $J/psi$  particle #${\vec {B}}=\,Magnetic\,Inductance$
46. $B=\,Baryon\,number$
47. ${\vec {M}}=\,Magnetization$
48. ${\mathcal {I}}=\,Spin$  and \htmladdnormallink{spin {http://planetphysics.us/encyclopedia/QuarkAntiquarkPair.html} Operator}
49. $EMF=\,ElectromagneticField$
50. $\mu =\,Magnetic\,Permeability$
51. $\chi =\,Magnetic\,Susceptibility$
52. $P=\,Parity$
53. ${\vec {P}}=\,Electrical\,Polarization$
54. $V_{E}=\,Electrical\,Potential$
55. $I=\,Electrical\,current$
56. $i=\,Current\,,Density$
57. $C=\,Capacitance$
58. $L=\,Inductance$
59. $\mathbb {I} =\,Impedance$
60. $R=\,Electrical\,Resistance$
61. $\displaystyle \E \, or\, \mu = \, Electrochemical Potential$
62. $a=\,activity$
63. $T=Temperature$
64. $\Delta H=\,Exchanged\,Heat$
65. $\displaystyle \L = \, Mechanical \, Work$
66. $S=\,Entropy$  (Thermodynamic state function)
67. $\Delta G=\,Gibbs\,Free\,Energy\,change$
68. $\Delta \mathbb {H} =\,Helmholtz\,Free\,Energy\,change$
69. ${\sigma }_{ij}=\,Pauli\,matrices$
70. $CQG=Compact\,Quantum\,Groups$
71. $QG={\mathcal {G}}=\,QuantumGroupoids$
72. $QCG=\,Quantum\,Compact\,Groupoids$
73. $QFG=\,Quantum\,Fundamental\,Groupoid$
74. $\displaystyle \A =\, Abelian \, category$
75. ${\mathcal {C}}=\,Category$
76. $\mathbf {G} =\,Group$
77. $\displaystyle \G = \, Groupoid$
78. ${\mathbf {G} }_{S}=\,Symmetry\,Groups$
79. ${\mathbf {g} }=Lie\,group$
80. ${\widetilde {\mathbf {g} }}=\,Lie\,algebra$
81. $SU=\,Special\,Unitary\,Groups$
82. K
83. 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