StuartFraser/WeNeedMoreLetters

One of the recent topics of conversation amongst undergrad MatScis? has been quite how many different things certain letters in the Greek and Roman alphabets can actually mean, and the great potential for confusion this creates. As part procrastination and a minor part revision aid, I thought I'd create a list of possibilities for each letter, in uppercase and lower case. At somepoint I might add the greek letters, or alternatively someone else might; if I didn't actively want other people to help out I wouldn't have put it on a Wiki, would I?

: Hebrew is possibly worthy of consideration. I know of at least Aleph and Bet from whatever my 4th year Set theory course was called - there are conceivably others. --CH

So, onwards. Due to the nature of the contributors this is heavily slanted towards cosmological and matierals science usage at the moment; this is an artefact and not an intention. I've ordered them by general broadness of utility, with a bias towards Materials terms because this page was originally intended as a revision aid for me after all.

Since a lot of people contribute to this page, and resolving conflicts is a pain, can I ask people to keep their edits at least five minutes apart? I've had six edit conflicts running now. Thanks. --SF

: An obvious solution to running out of letters is to use more of them. I nominate Dr. Seuss' extension: [picture of them] --Pallando

Roman Alphabet

Lowercase

a

Acceleration
Activity
Crystal lattice parameter
Dimensonless cosmological scale factor

b

Crystal lattice parameter
Impact parameter

c

Speed of light
Heat capacity
Constant of integration
Crystal lattice parameter

d

Diameter
Dipole moment
Distance
Derivative (as in dy/dx)

đ
Imperfect differential (which depends on the path taken- e.g. thermodynamic quantities like đQ and đW)

e

The transcendental number which is the base of natural logarithms
Electronic charge
Coefficient of restitution

f

Frequency (also nu)
Flux
Farad (unit of capacitance)
Function
Probability density function (also phi)

g

Acceleration due to gravity
Quantum degeneracy
Gyromagnetic ratio
Function (if f already used)

h

Planck's constant
Miller Index
Spatial distance, if x, y and z are in use (from 'height')
Function (occasionally, if f and g already used)

ħ

Planck's Constant/2π

i

The square root of -1
Current density
Miller Index in hexagonal 4-index notation
Index for tensors

j

Particle flux of any kind (also J)
Current density
The square root of -1
Index for tensors

k

Boltzmann's constant
"kilo-" (x10^3) prefix
Wavevector
Extinction coefficient
Miller Index
Quantum mechanical momentum
Distance in reciprocal space
Index for tensors
The square root of -1 (rare)
Many other empirical constants

l

Length
Miller Index
Index for tensors

m

Metres (unit of length)
"milli-" prefix (x10^-3)
Weibull modulus
Mass (usually of a small body, say a satellite or planet)
Apparent magnitude
Mirror plane
Nanotube chiral vector

n

Unknown integer value
Number of atoms/moles of a substance
Number density
Refractive Index
Polytropic index
Nanotube chiral vector

o

'Shrinks to zero with', by contrast with O and Ω
Not usable due to looking like a zero.

p

Probability
Momentum
Dipole moment vector
Unknown prime value

q

Electrical charge
(1 - Probability)
Deceleration parameter (cosmology)

r

Radius
Position
Product moment correlation coefficient

s

Displacement/Distance?
Seconds (unit of time)
Fibre aspect ratio in a composite
Index into a matrix

t

Time
Index into a matrix

u

Velocity before an event
Lattice vector

v

Velocity
Lattice vector

w

Lattice vector
Second complex unknown or variable (if z already used)
Fourth real unknown or variable value (if x, y, z already used)
4th-Dimension axis

x

Any real unknown or variable value
Position
Horizontal axis

y

Second real unknown or variable value (if x already used)
Vertical axis

z

Any complex unknown or variable
Third real unknown or variable value (if x, y already used)
Depth axis

Uppercase

A

Area
Amperes (unit of electrical current)
Hamaker Constant
Einstein A coefficient (atomic physics)
Magnetic vector potential
One of Oort's constants (Galactic dynamics)
The AckermanFunctions
Relative atomic mass

B

Magnetic Flux Density
Binomial distribution
Thickness (Fracture Mechanics)
Einstein B coefficient (atomic physics)
One of Oort's constants (Galactic dynamics)

C

Capacitance
Concentration
Coulombs (unit of charge)
Set of complex numbers (written double-struck, ℂ)
"Combination" binary operator (written <superscript-n>C<subscript-p>, for ways of choosing n objects from p, order-independant)
Constant of integration
Compliance

D

Diffusion coefficient
Electric displacement (epsilon nought E + P)
Covariant differentiation operator D/Dt?

E

Elastic Modulus (Young's Modulus)
Energy
Electric field
Expectation E(X) of a random variable (also double-struck, 𝔼(X))

F

Force
Free Energy (also G; depends on use of Gibbs or Helmholtz definitions)
Faraday's Constant
Face-centred lattice
Cumulative probability density function (also capital phi)

G

Free Energy (also F; depends on use of Gibbs or Helmholtz definitions)
Shear Modulus
Universal gravitational constant
"Giga-" prefix (x10^9)
Electrical Conductance
Bloch vector in hard condensed matter
Einstein tensor

H

Enthalpy
The H-field ( (one over mu nought) B + M)
Entropy (in information theory I can't believe they'd actually use a letter which means something different in thermodynamics, but it is possible --SF) (IIRC)
Heaviside function (zero from -infinity to 0, 1 from 0 to +infinity, integral of the Dirac δ function)

I

Current
Intensity
Moment of Inertia/Second? moment of Area
Information (IIRC)
Body-centred lattice
Generic or unknown integral

: It was almost an inevitability that I'd end up in a situation where the concept of "second moment of intensity" became relevant, wasn't it? --SF

J

Joules (unit of Energy)
Particle Flux (also j)
Total angular momentum
Current, usually in 4D

K

Kelvin (unit of Temperature)
Stress intensity factor
Equilibrium Constant
Constant of integration
Adiabatic constant

L

Avogadro's Constant (also N)
Orbital angular momentum
Inductance

M

"Mega-" prefix (x10^6)
Mass (usually of a large body, say a star)
Magnetisation of a material
Absolute magnitude

N

Newton (unit of force)
Avogadro's Constant (also L)
The set of natural numbers (written double-struck, ℕ)
Neutron number (A-Z)
Normal distribution

O

'Terms of order', as in O(x^2)
By extension, 'grows at the same rate as'

P

Pressure
Power (also W, allegedly)
Polarisation of a material
"Permutation" binary operator (written <superscript-n>P<subscript-p>, for ways of choosing n objects from p, order-important)
Primitive lattice
4-momentum (special relativity)
Probability of an event e.g. P(X = 0) (also ℙ(X = 0))

Q
Charge
Heat
Flow rate
Decay lifetime of a damped oscillation
Set of rational numbers (written double-struck, ℚ)

R

Resistance
Universal gas constant
Set of real numbers
Scale factor for the universe in general relativity
Riemann curvature tensor
Ricci Tensor
Ricci Scalar

S

Entropy

T

Temperature
Stress-Energy Tensor
Kinetic Energy

U

Internal Energy
4-velocity

V

Volume
Inverse square law field potential
Volts (unit of Electrical potential)

W

Watts (unit of Power)
Power (?someone justify this, please)I'm pretty sure I've seen it in textbooks, but can remove it if no one else agrees Do they? It strikes me as really odd because work is generally W and Power = d(Work)/dt
Weight
Work

X

A random variable (as in X is distributed normal 0,1)
Hydrogen mass fraction (astronomy)
Mole fraction (everyone else)

Y

A random variable (as in Y is distributed normal 0,1)
Helium mass fraction

Z

Atomic number / Proton number
Screened nuclear charge
Set of integers (written double-struck, ℤ)
Metallicity (anything other than H or He in astronomy!)
Partition Function
Normal distribution (random variable X ~ Z(0,1) )
A normal random variable Z ~ N(0,1)

Greek alphabet

Lowercase

α

Ferrite-like phase
Angle between b and c vectors in a unit cell
Fine structure constant
Primary line of an X-Ray emission spectrum
Helium-4 nucleus (α-particle)
Shorthand for GMm
Coherent state, as in a laser | α >

β

1/kT
Free election (β-particle)
Angle between a and c vectors in a unit cell

γ

Surface energy
Austenite phase
Lorentz factor
Photon
Shear angle
Ratio of heat capacities at constant pressure over at constant volume
Activity coefficient
Angle between a and b vectors in a unit cell.

δ

Small quantity
Crack tip opening displacement
Dirac delta function (infinite at 0, 0 everywhere else)
Kronecker delta δij (1 if i=j, 0 otherwise)

ε

Strain
Dielectric constant
Small quantity (less than γ)
Energy density
Interaction parameter
Alternating tensor / Levi-Civita epsilon (εijk = 0 if any two of i,j,k are equal; =1 if i,j,k are an even permutation of (i,j,k); =-1 if an odd permutation)

ζ

Zeta potential (I think this one wins a "duh")
Riemann's Zeta function (likewise)

η

Viscosity

θ

Often used for angles
Temperature
The polar angle in spherical polar co-ordinates

ι

Identity map (the map from a topological space X to itself, mapping every element to itself)

κ

Opacity
Index for tensors in GR
Thermal conduction coefficient

λ

Wavelength or other characteristic distance
Mean free path
Extensional viscosity
Index for tensors in GR
Parameter for defining lines in terms of vectors (as in x = a + λb)

μ

SI prefix "micro" (10^-6)
Relative molecular/atomic mass
Magnetic permeability
Chemical potential
Coefficient of friction
Shear modulus (also G)
Muon (A lepton charge -1 heavier than an electron).
Charge carrier mobility
Index for tensors in GR
Parameter for defining planes in terms of vectors (as in x = a + λb + μc)

ν

Frequency
Kinematic viscosity = η / ρ
Neutrino
Index for tensors in GR

ξ
ο

π

The ratio between the circumference and diameter of a circle (for mathmos)
3.1415926..... (for physicists)
3 (for engineers)
Of order unity (for Sanjoy)
A measure of the likely future of the universe (for people doing general relativity with very long rulers)
The pion or pi meson
The prime counting function π(n)

ρ

Density
Resistivity
Index for tensors in GR

ς

σ

Stress (generally tensile or hydrostatic)
Standard deviation
Conductivity
Stefan-Boltzmann constant
Surface energy (also gamma)
Surface coverage
Cross-section of interaction.

τ

Characteristic timescale.
Shear Stress
Often used for a second time variable
Tauon (a lepton charge -1, heavier than the electron and muon)
Proper time in relativity (that is, time in a frame stationary and unaccelerated with respect to the clock)

υ
φ

The Golden Ratio, (1+sqrt(5))/2
Used for angles (if θ is in use)
The equatorial angle in spherical polar co-ordinates
Probability density function (sometimes specifically the one for the Normal distribution)

χ
Chi-square test
Magnetic susceptibility (per site, if Χ is in use)

ψ

Wavefunction in quantum mechanics

ω

Angular Frequency
Rotation tensor
The infinity which is the number of natural numbers (also aleph_null)
An event in Ω in probability/measure

Uppercase
Α
Β
Γ

Continous function which has the same values as ! (factorial) for integers
Affine connection (GR)
Transition rate (QM)

Δ
Change in value of a quantity.

Ε
Ζ
Η
Θ
Ι
Κ
Λ
Cosmological Constant

Μ
Ν
Ξ
Ο
Π
Product

Ρ
Σ
Sum

Τ
Υ
Upsilon particle in particle physics

Φ
Cumulative probability density function (sometimes specifically the one for the Normal distribution)
Gravitational Potential
Magnetic Scalar potential
Wavefunction, when Ψ is in use

Χ
Magnetic Susceptibility

Ψ
Wavefunction, especially in quantum mechanics

Ω
Ohms (unit of resistance)
Number of microstates corresponding to a single macrostate.
Ratio of density of Universe to Critial density. Often subscripted for matter, radiation, dark energy, curvature,....
'Grows faster than', as in y = Ω(x). Contrast with O and o.
The event space in probability/measure

SeeAlso [this xkcd T-shirt]

CategoryAbbreviation (erm, I think. CategoryLotsOfAbbreviations doesn't exist.)