[Dylan16807]

Can you explain what this notation is: p^\mu = m u^\mu

What's the backslash, is that m times u or μ, is that exponentiation, which are vectors and which are scalars?

[tfgg]

It's latex notation and should render like http://arachnoid.com/latex/?equ=p%5E%5Cmu%20%3D%20m%20u%5E%5... . It's a bit obtuse to be using it on a non-physics/maths forum.

mu is being used as an index (mu=0,1,2,3) on the components of the vectors p and u, m is a scalar representing rest mass.

[sqrt2]

p^μ is the μ-th component of the vector p, and in an equation p^μ = m u^μ, μ is to be taken as a free variable, i.e. the equation is true for every μ. In relativity, Greek indices are taken to range over time and the three spacial dimensions (whereas Latin indices only range over the spacial dimensions).

This notation can be naturally extended to tensor products of vectors in the tangential and co-tangential spaces to the base manifold that is spacetime (simply called "tensors" by physicists): https://en.wikipedia.org/wiki/Einstein_notation