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

#### Fundamental Constants in Physics

• ${\displaystyle c=\,magnitude\,of\,\,light\,velocity}$  in vacuum
• ${\displaystyle {\epsilon }_{0}=\,dielectric\,constant}$ , or electrical permitivity of vacuum
• ${\displaystyle {\mu }_{0}=\,magnetic\,permitivity\,(or\,permeability)}$  of vacuum
• ${\displaystyle h=\,Planck's}$  constant
• ${\displaystyle k=\,Boltzmann}$  constant
• ${\displaystyle n=\,Avogadro's\,number}$
• Electron mass (at rest), ${\displaystyle e}$
• Proton mass (at rest) ${\displaystyle m_{P}}$
• Fine-structure constant , ${\displaystyle \alpha \,}$ , is the emf coupling constant (that characterizes the strength of the electromagnetic interaction); ${\displaystyle \alpha \,=\ 7.297\,352\,570(5)\times 10^{-3}\ =\ {\frac {1}{137.035\,999\,070(98)}},}$  (i.e., approximately ${\displaystyle {\frac {1}{137}}}$ )
• Neutrino masses (at rest), ${\displaystyle m_{\nu }}$
• Electron charge, ${\displaystyle m_{e}}$
• Electron Magnetic Moment, ${\displaystyle \mu _{e}}$
• Proton Magnetic Moment, ${\displaystyle \mu _{p}}$
• neutron Magnetic Moment, ${\displaystyle \mu _{n}}$
• Gyromagnetic Ratios of nucleons or Nuclei, ${\displaystyle \gamma _{n}}$
• gyromagnetic ratio of the Electron, ${\displaystyle \gamma _{e}}$
• Gyromagnetic Ratio of the Muon, ${\displaystyle \gamma _{\mu }}$
• ${\displaystyle G=\,Universal\,Gravitational\,Constant}$
• ${\displaystyle \lambda =\,Cosmological\,Constant}$  (introduced by Einstein in Relativity Theory)
• C
• D
• E