Why \(x_{\dot{\alpha}\alpha}\)? What is this object? For the Lorenz transformation \(P^\mu \to \tensor{\Lambda}{^\mu_\nu} \rho^\nu \equiv \rho^{\prime \nu}\): \[ \begin{aligned} P_{\alpha \dot{\alpha}} &= x \rho^{\mu}\sigma_{\mu \alpha \dot{\alpha}}\\ &= MpM^\dagger \end{aligned} \] Using \(P^mu\rho_\mu = \det{p}\), the following can be obtained: \[ \begin{aligned} \det{MpM^\dagger} &= \det{p}\\ \det{M}\det{p}\det{M^\dagger} &= \det{p}\\ \det{M} &= 1 \end{aligned} \] Expanding on this,…

## GWs: General introduction

The topic I would like to ask or interrogate is how fourier analysis is used to sort out and measure the effects of a black hole merger by measuring the effects of GWs stretching and bending the arms of an interferometer. A few pointers to get the audience interested in what GW’s are: Gravitational waves are…

## Two approaches to researching GWs.

For two of my modules this semester, we have been given free reign over the choice of topic – so I am using this opportunity to delve further into gravitational waves. One aspect I will approach this from a numerical and mathematical approach, and the other will be an essay approach. I would like to…