I read several articles saying that most mathematicians have the peak of their career before 30 and after that they don't do much significant work. Although this is a simplification of the reality, the truth is that in math many people do major breakthroughs before 30, a lot more than in other...
Homework Statement
Calculate the Casimir force in 1D using a Gaussian regulator.
Homework Equations
The Attempt at a Solution
I reached a point where I need to evaluate a sum of the form $$\sum_n n e^{-\epsilon^2n^2}$$ Can someone help me? I didn't really find anything useful online. I...
Hello! In Schwarz's QFT he introduces in chapter 27 the Spin-Helicity formalism as a way of calculating gluon-gluon interactions much easier than going through all the Feynman calculus from the beginning to the end. It seems so amazing, but I am not sure I understand what is the fundamental...
But I am not sure how does he get the first and last terms. He gives a formula for ##\Phi_i##, but ##|0>## is not an eigenstate of ##\hat{\Phi}(x,t)##. What confuses me the most is why don't we have boundary terms for the integral. In QM you have boundaries the for the beginning and end points...
I am not sure about anything right now... But as I said in the post I can't see where he is using the fact that the initial and final sates are the vacuum so technically you would get the same answer no matter what your initial and final states are, which doesn't really make sense to me.
Hello! I am reading from Schwarz book on QFT the Path Integral chapter and I am confused about something. I attached a SS of that part. So we have $$<\Phi_{j+1}|e^{-i\delta H(t_j)}|\Phi_{j}>=N exp(i\delta t \int d^3x L[\Phi_j,\partial_t \Phi_j])$$ What happens when we have the left and right...
So, if helicity is not a good quantum number for massive particles and in the massless case helicity is the same as chirality, why do we need helicity in the first place. Why don't we just use chirality?
Yes, that is the book I am using. So in 5.3 as far as I can tell is mainly using helicity...
Hi! I am kinda confused about what gets conserved in QED and what not. So the chirality is always conserved, I got that. So in the massless limit, helicity is too. Now in the massive limit. Are spin and helicity conserved? And if they are, are they at each interaction vertex, or just overall...
Hello! We derived the electron proton scattering differential cross section using QED and I noticed that the equation doesn't depend on the impact parameter. Using classical EM one can calculate the deflection of an incoming electron as a function of the impact parameter, so I was wondering how...
Hello! I am reading some QFT and it is a part about how causality implies spin-statistic theorem. In general, one needs 2 observables to commute outside the light-cone. For scalars, we have $$[\phi(x),\phi(y)]=0$$ outside the light-cone, and by using the operator form of the field you get that...
I tried, but I am confused at certain steps. I would normally post here what I did so far and ask for help, but I am sure they are derived in some book already (also typing down everything would be quite time consuming as there are many indices).
Thank you! That is the book I am using actually and I am at that chapter, but in that book the rules are just listed, I would like a full derivation, the same way it is done in previous chapters for the ##\phi^3## interaction.