Recent content by lalo_u

In ##SU(2)## symmetry, we can define a triplet as ##2\otimes 2^*=3\oplus 1## with a tensor representation like this: $$q_iq_j^*=\left(q_iq^j-\frac{1}{2}\delta_j^iq_kq^k\right)+\frac{1}{2}\delta_j^iq_kq^k.$$ The upper index denotes an anti-doublet and the traceless part in parentheses represents...

Thanks @vanhees71 i agree with your calculation. However I was insisting on the calculation of Pokorski, and redefine the projection operator in Coulomb gauge as follows...

Thank you Avodyne, but there are two more things, a) we are calculating the photon free propagator, is it correct considering any interaction?, b) what about the extra ##\delta_{\alpha\beta}## at the beginning of the expression?

My aim is to derive the photon propagator in an Coulomb gauge following Pokorski's book method. In this book the photon propagator in Lorenz gauge was obtained as follows: 1. Lorenz gauge: ##\partial_{\mu}A^{\mu}=0## 2. It's proved that ##\delta_{\mu}A^{\mu}_T=0##, where...

If you read it again, the first component of de field has been removed, so it's Coulomb. I'm trying to do this method, because seemed ellegant to me: it's done covariantly, even though we are dealing with Coulomb. :smile:

My aim is to derive the photon propagator in an Coulomb gauge following Pokorski's book method. In this book the photon propagator in Lorenz gauge was obtained as follows: Lorenz gauge: ##\partial_{\mu}A^{\mu}=0## It's proved that ##\delta_{\mu}A^{\mu}_T=0##, where...

Sorry for my english, I realize i don't let me understand when I use the word expand. I used it in the sense of "calculate something" like the command in "Mathematica". But you've got the point of my question ChrisVer, when you wrote "Linear algebra can't help... the gammas are 4x4 matrices...

I mean for example: \left(\bar{\psi}^L_{\nu_l},\bar{\psi}^L_l\right) \begin{pmatrix} 0 & \sigma_k \\ -\sigma_k & 0 \end{pmatrix}\partial_{\mu} \begin{pmatrix} \psi^L_{\nu_l} \\ \psi^L_l \end{pmatrix} Are we forbidden to expand this? I'm pretty sure you're right like all the QFT books. I'm...

Yes. I understand what you're saying about the different vector spaces ChrisVer. But if you expand the SU(2) doublet we have the same operation but now with singlets, isn't it?

I was trying to prove all those little things you spend long as the local invariance in the free Lagrangian of electroweak interaction. Taking into account the appropriate SU(2) transformations (without covariant derivatives), came to the following expression \mathcal{L}_{\text{ferm.}} =...

Well, i´m trying to understand this: I´ve got a representation of SU(2)_L\otimes U(1)_Y such that the left lepton doublets can be represented as (2, -1) and lepton singlets rights as (1, -2). Then I can be left antiparticles bilinear representations as (2,1)\times(2,1) or...

Ok. Firstly we should assume these capacitors are completely charged. So, we cannot talk about any current in the circuit (the charges don't jump the capacitors). Secondly, the 24 V power supply is greater than the other one. Then, we must assume that Va > Vb and the "minus sign" of book answer...

I got it, Andrien. I had shown only for the full Majorana fermion, and not for any of their helicities that was what I wanted. I considered its components, as you suggested, and I did. Thank you.

You're dividing a quarter of an arc between a full arc angle...