Recent content by AndrewGRQTF

Why does the Kronecker being invariant mean that the ##R \otimes \overline{R}## can be decomposed into a direct sum of the singlet representation and other irreps?

I don't understand what the last paragraph of the attached page means. Why does the Kronecker delta being an invariant symbol mean that the product of a representation R and its complex conjugate representation has the singlet representation with all matrices being zero? Doesn't the number...

Thanks a lot. I learned something important: not to forget about the argument of a function

How is my friend right?

Ok, thanks for your replies. Why is BvU saying what he's saying?

But how is ##\frac {dg}{dw} \ne \frac {d}{dw} f(q,-w)##? It is given that ##g(q,w) = f(q,-w)## so we just take the derivative of both sides? Writing out the derivative we have $$\frac{g(q,w+\Delta w) - g(q,w)}{\Delta w} = \frac{f(q,-(w+\Delta w)) - f(q,w)}{\Delta w}$$ as ##\Delta w \to 0##

If we have an equation ##g (q,w) =f(q,-w)## and we want to find the derivative of that equation with respect to w, we would normally do $$\frac {dg}{dw} = \frac {d}{dw} f(q,-w) = \frac {df}{d(-w)} \frac {d(-w)}{dw} = -\frac {df}{d(-w)} $$ but my friend is saying that $$\frac {dg}{dw}= -\frac...

Take for example dimensional regularization. Is it correct to say that the main point of the dimensional regularization of divergent momentum integrals in QFT is to express the divergence of these integrals in such a way that they can be absorbed into the counterterms? Can someone tell me what...

It is commonly said that the speed of light when traveling inside materials is lower than that of light in vacuum, but I don't understand how this can be true. It is the same light traveling, so how can it act differently? Does light appear to be slower in materials because it is not following a...

As has been pointed out by TSny, the ##A^*A## should be an overall factor of the probability density. You made another mistake multiplying the exponentials when finding the probability density: don't you know that ##e^a e^b = e^{a+b}## and not ##e^{ab}##?...

Here is additional information

Let's say we have a Dirac field ##\Psi## and a scalar field ##\varphi## and we want to compute this correlation function $$<0|T \Psi _\alpha (x) \Psi _\beta (y) \varphi (z_1) \varphi (z_2)|0>$$ $$= \frac {1}{i} \frac{\delta}{\delta \overline{\eta}_\alpha(x)} i \frac{\delta}{\delta \eta_\beta(y)}...

On the right hand side, since we wrote out the T which are matrices, is the ##F_{\mu \nu} ^a## a number? For example is ##F^1_{22}## a number?

So is this true: ##F^2 = (F^{\mu\nu}F_{\mu\nu}) \Sigma_a (T^aT^a) ## where the a goes from a=1,...,n and the n is the number of generators of the group? This the the ##F^2## that we put inside the trace, right?

I am sorry for asking this stupid question, but in the Yang-Mills lagrangian, there is a term ##Tr(F^{\mu \nu}F_{\mu \nu})##. Isn't ##F^{\mu \nu}F_{\mu \nu}## a number?