Recent content by Siupa

Consider a system of two identical spin zero particles on a sphere. Let ##\vec{L} = \vec{L}_1 + \vec{L}_2## be the total orbital angular momentum of the two particles, and ##l_1, l_2## be the orbital angular momentum quantum numbers corresponding to particle 1 and particle 2. Consider the...

Well, whatever you and I are in real life, in this context you’re in a position of authority with respect to me, as you’re a respected member of the community who’s giving me help and I’m a relatively new member with little questions asked and no help given on the forum. But that’s besides the...

I’ve been nothing but thankful to everyone who answered here, I’ve thanked him multiple times in that same message you quoted. His comment about beginner students being unwilling to accept that sometimes books might be wrong was indeed condescending and out of context, even if in good faith...

that’s probably it yes, the author must have imagined it as a continuation of the premises of the previous question, but it’s not clear given that point (c) isn’t intended/nested hierarchally under (b), but instead is presented in parallel as “the next question”. Thanks!

You’re right, that was easy to check in hindsight. There’s at least one other frame where the process can happen with all equal masses, yet that relationship doesn’t hold. Thanks for your help! There’s no need for that condescending lesson about being afraid to confront authority though: I’m...

What are you referring to? Can you clarify what would have been more clear about my question, had I followed a homework template? As for your question, it’s clear from the notation what kind of absolute value the text of the problem is talking about: 4 vectors are introduced in the first line...

Yes, with the extra assumption that ##|\bf{p}_1| = |\bf{p}_2|## I can solve this. Let’s call ##\bf{p}_i := \bf{p}_1 = \bf{p}_2##. Then, ##\bf{p}_1 + \bf{p}_2 = 0 = \bf{p}_3 + \bf{p}_4## implies ##|\bf{p}_3| = |\bf{p}_4|##, and we can also call either of these ##\bf{p}_f##. To get our result we...

Are you suggesting this as an hint on how to prove it, or are you suggesting that the question is wrong?

Stuck on (c), part (i). Any ideas about what is the most elegant way to prove it, maybe using Mandelstam variables since this exercise is supposed to be about them?

I'm looking at a proof of beta function universality in ##\phi^4## theory, and at one point they do the following step: after imposing that the renormalized coupling ##\lambda## is independent of the cutoff ##\Lambda##, we have $$0= \Lambda \frac {\text{d} \lambda}{\text{d} \Lambda} = \Lambda...

Let ##\Gamma[\varphi] = \Gamma_0[\sqrt{Z}\varphi ] = \Gamma_0[\varphi_0]## be the generating functional for proper vertex functions for a massless ##\phi##-##4## theory. The ##0## subscripts refer to bare quantities, while the quantities without are renormalized. Then $$\tilde{\Gamma}^{(n)}(p_i...

I don't think that this falls under the definition of "homework", but maybe I didn't read the description of each forum well enough, if that's the case, apologies. As for showing my attempt at a solution, I think I did, I described my first steps with changing variables and then integrating the...

Thank you, yes, that actually works if one takes care with putting an upper cutoff and then taking the limit afterwards. I will try the other method that the other user proposed with Feynman parameters, but in any case this works. Thank you!

Unfortunately partial fraction decomposition doesn't work: the original integral converges, but after PFD you get two divergent integrals. I'm sure that the divergences "cancel out" to give the same finite result that you would have got without PDF, but to handle the two new individually...

I need to prepare for an oral exam for a course in QFT. If my professor asks me to derive the 1-loop renormalization of the 2-point function in phi^4 theory, they expect me to be able to follow through the steps and arrive at a result. I don't think they'll be satisfied if I answer with "let me...