Recent content by eoghan

It makes sense! Thank you for checking it out and for the hints :)

Thank you for checking. 1. Correct, ##d## must divide ##n##. I need to specify this better. 2. Yes, this needs an explanation. I was simply supposing that if ##n## is not prime, then there exists a prime number that divides ##n##. But this is a consequence of the FTOA, that I am trying to prove...

I was intrigued by a comment in Brilliant.org: Besides the proof provided by Brilliant, I also found a couple of other websites. But none of these proofs were entirely clear to me. So I tried to come up with my own proof. Since I am not a group theorist, I wanted to ask if the proof makes...

My idea goes like this. Let's suppose there is an observable ##A## with eigenvalues ##a_1##,...,##a_n## and eigenvectors ##|a_1\rangle##,...,##|a_n\rangle##. Our state is described by a state vector ##|\Psi\rangle##. The probability to measure the value ##a_1## for ##A## is then given by $$...

Hi there, In QM it is said that state transformations must be implemented via unitary operators. The reason is that, if ##\left| \Psi\right\rangle## is a normalized state and ##U## is a unitary operator, than ##U\left|\Psi\right\rangle## is also normalized. But why do I need...

Hi everyone, In his book "Quantum field theory and the standard model", Schwartz derives the position-space Feynman rules starting from the Schwinger-Dyson formula (section 7.1.1). I have two questions about his derivation. 1) As a first step, he rewrites the correlation function as $$...

@PeterDonis Very nice answer, now it is clear to me why the Hilbert space (Haag's theorem apart) is supposed to be the same. @vanhees71 Nice book. I just had a look at its content on Amazon and it's definitely on my list once I will be done with the Schwartz!

Hi there, In his book "Quantum field theory and the standard model", Schwartz assumes that the canonical commutation relations for a free scalar field also apply to interacting fields (page 79, section 7.1). As a justification he states: I do not understand this explanation. Can you please...

Thank you very much for all your answers :)

Hi there, In QFT, a free scalar field can be represented by the lagrangian density $$\mathcal{L} = \frac{1}{2}\left(\partial\phi\right)^2 - \frac{1}{2}m^2\phi^2$$ I would like to find a classical system that has the same lagrangian. If we consider the transversal motion of an elastic string...

Hi there, While reviewing the theory of Feynman diagrams for QED, a question came into my mind. In the textbooks, one usually deals with processes involving two incoming particles. But I could imagine a process where four particles are interacting (e.g. attached picture) and this can give a...

I've read something about this equation, but still I don't get why we cannot use it. It has to do with the fact that, as pointed out by vanhees71, with such an equation the on shell condition is not met? Thanks for the reference, I admit my knowledge of group theory is still in its infancy. I...

Hi there, I just saw some lectures where they claim that the Klein Gordon equation is the lowest order equation which is Lorentz invariant for a scalar field. But I could easily come up with a Lorentz invariant equation that is first order, e.g. $$ (M^\mu\partial_\mu + m^2)\phi=0 $$ where M is...

Thank you everybody for the answers and the interesting discussion that followed! I got really helpful insights :)

I think this is what confuses me... what does the coordinate time represent? Or, you say that an object that doesn't move in space has a ds which is ##\sqrt{1-v^2}d\tau##, so this is the time reported by a clock at rest. But what is not clear to me is: ##ds## is just an abstract quantity which...