I disagree, because translational invariance tells us that if all coordinates go to infinity together the S matrix should be invariant.
I think I solved the problem yesterday, when you integrate expression (with this 3-spacial delta) 4.3.8 the exponentials become "coupled" i.e. if you integrate...
Im following Weinberg's QFT volume I and I am tying to show that the following equation vanishes at large spatial distance of the possible particle clusters (pg 181 eq 4.3.8):
S_{x_1'x_2'... , x_1 x_2}^C = \int d^3p_1' d^3p_2'...d^3p_1d^3p_2...S_{p_1'p_2'... , p_1 p_2}^C \times e^{i p_1' ...
Hi all,
I'm trying to find a mathematical way of showing that given a complete set $$\left |a_i\right \rangle_{i=1}^{i=dim(H)}∈H$$ together with the usual property of $$\left |\psi\right \rangle = ∑_i \left \langle a_i\right|\left |\psi\right \rangle\left |a_i\right \rangle ∀ \left...
Hi everyone,
I want to generate 8 random variables (in reality to form 4 complex numbers) such that the sum of the 8 variables squared is equal to unity. The aim of generating such numbers is to perform a quantum simulation of 4 qubits (thus the 8 parameters). I've been trying to use...
Thank you so much! Could you explain how this is done in n-space, (I can't really picture k-space) or perhaps refer to a book that does that, I am struggling to find any alternative derivation!
Thanks in advance! :)
I am trying to understand the derivation for the DOS, I get stuck when they introduce k-space. Why is it necessary to introduce k-space? Why is the DOS related to k-space? Perhaps if someone could come up to a slightly different derivation (any dimensions will do) that would help.
My doubt ELI5...
Dear physics forums,
What is the physical interpretation of imposing the following constrain on a Hamiltonian:
Tr(\hat H^2)=2\omega ^2
where \omega is a given constant. I am not very familiar with why is the trace of the hamiltonian there.
Thanks in advance,
Alex
Okay, I first let you know my original attempt to comment on my procedure:
Let dist(\psi,\phi) = || \psi - \phi || = \sqrt{ < \phi, \phi> + < \psi, \psi> - 2 || < \psi, \phi> ||} which is a metric.
now dl = dist(\psi+d\psi,\phi) = \sqrt{ < \phi, \phi> + < \psi +...
Okay,I think I just proved that (even though its not Fubini-Study metric) || |\psi>-|\phi> || is a metric aswell, as it satisfies d(x,y)≥0 , d(x,y)=0 ↔ x=y, d(x,y)=d(y,x) & d(x,z)...etc. is this the case? or have I made a mistake?
Okay I see now what you mean now, yeah I agree it's quite confusing the notation. Either way I would be very grateful if you could give me a hand with this derivation by quicking off with the first steps please!
Thanks beforehand!
But why then is it called the distance between those two points?
I think I know what you are saying: take the inner product and solve for the angle, then you get the arccos, but in the article I sent it was referred as the length. Moreover the ultimate aim of doing this is to derive the ds...
Hello PF!
I was reading
https://en.wikipedia.org/wiki/Fubini–Study_metric (qm section like always :wink:)
And can't figure out how to derive:
\gamma (\psi , \phi) = arccos \sqrt{\frac{<\psi|\phi><\phi|\psi>}{<\psi|\psi><\phi|\phi>}}
I started with
\gamma (\psi , \phi) =|| |\psi> - |\phi>||=...
I'm very interested in quantum mechanics and electromagnetism so I guess QFT could be my cup of tea, and definitely this is exactly one of the branches you can choose in this uni I'm applying...
Hi everyone!
I am currently in the process of applying for a masters degree in theoretical physics. I am having troubles on writing the personal statement part since I really need to make it shine (200 applications and 20 places:frown:) . Any definitely do's and dont's I should bear in mind?
A...