1.7 Four vectors Flashcards
What do four vectors represent?
A physical quantity
What two rules must all four vectors obey?
Must respect space-time symmetry
Must obey LTs
Which script is covariant and contravariant?
Contravariant - superscript
Covariant - subscript
What do we mean by an invariant quantity?
It is the same in all frames of reference
What is x^μ equal to?
(ct, x, y, z)
What is x_μ equal to?
(ct, -x, -y, -z)
How can we calculate the invariant scalar of a four vector?
Multiply the contravariant and covariant parts together
x^μ * x_μ
What is the four velocity equal to?
u^μ = γ(c, v)
= c and the 3 velocity vector
What is the invariant scalar of the velocity equal to?
c^2
What is the four momentum equal to?
p^μ = (E/c. p)
= E/c and the 3 momentum vector
What is the invariant scalar of the momentum equal to?
(mc)^2
What is the four current equal to?
j^μ = (ρc, j)
= charge density * c and the 3 current vector/density
What is the four potential equal to?
A^μ = (Φ/c, A)
= scalar potential/c and the 3 vector potential
In the Lorenz gauge, what is the d’Alembert operator acting on A equal to?
◻A = μ_0 j
In the Lorenz gauge, what is the d’Alembert operator acting on Φ equal to?
◻Φ = ρ/epsilon_0 = ρc/epsilon_0 c
