4 vectors

1. I Invariant Mass in a Gravitational Field

In Special Relativity, you learn that invariant mass is computed by taking the difference between energy squared and momentum squared. (For simplicity, I'm saying c = 1). m^2 = E^2 - \vec{p}^2 This can also be written with the Minkowski metric as: m^2 = \eta_{\mu\nu} p^\mu p^\nu More...
2. I The relativistic de Broglie equation

I'm having trouble understanding how the 4-wave vector is derived, and also how it is then used alongside the 4-momentum vector to formulate the relativistic de Broglie equation. The inner product of the 4-momentum vector with itself, is an invariant quantity. If we define the 4-momentum...
3. I 4 vector upper and lower indices

I'm working through some intro QFT using Peskin accompanied by David Tong's notes, and have a question over notation. From Peskin I have: x^\mu=x^0+x^1+x^2+x^3=(t,\mathbf{x}) and x_\mu=g^{\mu\nu}x^\nu=x^0-x^1-x^2-x^3=(t,-\mathbf{x}) so p_\mu p^\mu=g^{\mu\nu}p^\mu p^\nu=E^2-|\mathbf{p}|^2...