Lorentz according to Bamberg & Sternberg

Cantab Morgan

A number of times in Physics Forums, I've read recommendations for the excellent book, A Course in Mathematics for Students of Physics by Bamberg and Sternberg. In their chapter 4.6 on Special Relativity (page 152 in my edition), they prove that the Lorentz scalar product is left invariant under Lorentz transformations. Unfortunately, I find this proof impenetrable because they abruptly introduce variables p and q, which they have never defined. It looks like some kind of editing or copy-and-paste mistake.

Does anybody have any insight into what they were driving at, and what those p and q variables are? It seems that they are not the traditional momentum and position variables in this case.

HallsofIvy

I don't have that book but it sounds to me like the Lagrangian formalism. p and q are "generalized coordinates" with q representing position and p momentum. You might do better in the generala physics forum than mathematics.

George Jones

On page 151, [itex]p[/itex] and [itex]q[/itex] are defined as (something like) lightcone coordinates, [itex]p = \left( x - t \right) /2[/itex] and [itex]q = \left( x + t \right) /2[/itex].

Cantab Morgan

Aha! Thank you so very much, George!