Recent content by kevinferreira

Yes you should also use the fact that the matrices should be linearly independent (they form a so(3) basis). The commutation relations give you 3 equations, plus if needed you can use the fact that the sum of the squares must be prorportional to the identity. You should be able to find them...

Look for 'gauge theory' in any good qft book, or just google it.

Just because two things study the same phenomena it doesn't mean one of them is part of the other. They can study these phenomena in different perspectives. Theology and physics both study the universe as a whole and its fundamental properties but neither physics is a part of theology or...

It is telling you that the term with x^n after doing the multiplication comes with a factor of 1 because it is the result of multiplying the n x's and all of them have a factor of 1! And 1^n=1. Try with n=2 and then n=3.

First let formulate the question precisely. Classical vacuum or quantum vacuum? And 'heat death universe' vacuum or idealised vacuum? That is, very few particles/energy in a bigger and bigger volume or one fixed volume with zero particles/energy in it? (I don't know how much equivalent...

That's the whole point of the exercise, to see that the exponentials do not combine to give 1. To do such a thing, you would have to pass exp(i\alpha\sigma^z) to the other side of \sigma^x. But \left[\sigma^z,\sigma^x\right]\neq0 so that you can't simply commute them. Hint: express the...

I don't know what to consider as 'microstates' when there is nothing to construct microstates with! A classical vacuum, with no particles nor anything, may not even have an assigned entropy! An alternative (instead of letting the number of particles N go to zero) is to demand instead that the...

I would say the electromagnetic field (or more precisel, the electromagnetic potential field) exists in all space-time. This is the usual quantum field theory theoretical basis (not only for photons, but all particles too) which is used to construct the standard model. Also, a photon cannot...

Let's consider the macroscopic state "1 particle in a volume V". This is a pretty good vacuum. What is the number of microstates compatible with this? Counting: the particle can be anywhere within the volume V, so it W has to be proportional to V, in my opinion.

Why would the vacuum have zero entropy? Use the statistical definition S=k_B~log(W) where W is the number of micro-states compatible with a vacuum. Now, you're saying there's only one of these micro-states. What does this mean?

Replace x\rightarrow -x. If the integrand transforms f(x)\rightarrow f(-x)=-f(x) then it is odd.

1.) You have to show that the 8 properties hold. The linear combo idea, as you call it, is a consequence of those properties. Simply showing that a linear combination of elements is still an element does not prove that the set is a vector space. Take for example the real 1-dimensional euclidean...

It is called the equivalence principle which, together with the relativity principle, make up the whole theory. The equivalence principle says as Einstein himself wrote. This allowed him to conceive the idea that maybe gravitation was indistinguishable from an inertial effect, when seen...

What about the electric and magnetic fields created by the electron?

It doesn't really make a difference. Yes, indeed, the first derivative vanishes at 0, but it doesn't make a difference because we're interested only in the zero order, so what I wrote holds anyway (an O(x^2) is an O(x) ). Regarding the parenthesis, it makes no difference whatsoever, the...