Dork Scratchings

Lockdown reading My lockdown reading list consists of just one book. This might last a long time I thought, so it's my opportunity to make a 2nd stab at understanding Quantum Field Theory. Last time, I bought "Quantum Field Theory for the gifted Amateur" and I learned a lot from it. Mainly that I am not gifted! I got three chapters through it and then gave up on the book, and on quantum field theory. This time round I did my research better and found a much more gentle book: Student Friendly Quantum Field Theory, by Robert D. Klauber . It covers the same material, but takes pains not to lose the reader, by spelling out every ambiguity and subtlety. I'm half way through and feeling quite chuffed with myself. Here I am studying hard, on a sunny day in Lockdown Britain: No, the weights are not mine In this book, and every other in the QFT literature there is a concept of some particles being virtual. What's this about?  Why are some virtual and o...

Most Quantum Mechanics courses try to avoid imposing any kind of interpretation. This makes sense since the interpretation of QM is controversial but the mathematics is not. Unfortunately a little bit of interpretation always sneaks in through the back door. Whether you're being taught the Schroedinger Equation, Feynman path integrals, or QFT, the assumption is always that you can divide reality into That Which Is Under Study and the Rest Of The World... and that the nature of reality in the two parts is entirely different. If it's the Schroedinger Equation being taught That Which Is Under Study is represented by a state vector in a Hilbert Space that evolves with time; with Feynman Path integrals That Which Is Under Study is the set of all legal Feynman diagrams which complete the picture by joining neatly with the  diagram for The Rest Of The World; if it's QFT then the nature of reality inside That Which Is Under Study is a single state vector which can be converted in...

The following equation can be viewed in a couple of ways $$ action =  \int_{\Omega} \mathcal{L} (\phi_a, \partial_{\mu}{\phi_a}) d^4x $$ 1. Classically Every physical law can be written in terms of an Action Principle .  An action principle states that measurable values $\phi_a(\mathbb{x},t)$ over a region of spacetime $\Omega$ will be such that the action is stationary.  Or to put it another way, if you infinitesimally deform the $\phi_a$ then either  however you do it the action will increase, or  however you do it the action will decrease. There is an important caveat though: the action is stationary because we only consider deformations of the $\phi_a$ that preserve its values on the boundary $\partial \Omega$. This is an alternative to the differential way of describing the universe, in which only a single point of spacetime is considered.  In the differential formulation, instead of being told the values of $\phi_a$ on a boundary of a r...