Lorentz group Definition and 68 Threads

Hi! In Weinberg's book "The quantum theory of fields", chapter2, it states that the transformation of a massive particle is U(\Lambda)\Psi_{p,\sigma}= N\sum\mathcal{D}^{(j)}_{\sigma',\sigma}(W)\Psi_{\Lambda p,\sigma'} where W is an element in the little-group SO(3). But than it states that...

The words Poincare and Lorentz sound pretty elegant. I think they are French words like Loreal Or Laurent. I know Poincare has to do with spacetime translation and Lorentz with rotations symmetry. But how come one commonly heard about Lorentz symmetry in Special Relativity and General...

Hello, I'm studying the Lorentz group and their properties... and I have some question for them.. Peskin's text(p496) said that "we are primarily interested in Lie algebras that have finite-dimensional Hermitian representations, leading to finite-dimensional unitary representations of the...

This is something I feel I should know by now, but I've always been very confused about. Specifically, how does one determine what each representation of the Lorentz group corresponds to? I mean, I know that the (1/2,0) and the (0,1/2) representations correspond to right and left handed spinors...

we all know the lorentz group is of four disconnected components about the component connected to the unit element, is it coverable with single-parameter subgroups? put it in another way are all the elements in this component of the form exp(A)? i am studying relativistic quantum...

I'm reading the wiki article on Representation theory of the Lorentz group and they seem to make a distinction between these two reps: (1/2,1/2) and (1/2,0) + (0,1/2) I did some checks and it seems that these two are the same. Am I wrong or is the wiki article wrong (won't be the...

I'm very confused By performing a lorentz transformation on a spinor \psi\rightarrow S(\Lambda)\psi(\Lambda x) and imposing covariance on the Dirac equation i\gamma^{\mu}\partial_{\mu}\psi=0 we deduce that the gamma matrices transform as S(\Lambda)\gamma^{\mu}...

This is probably very trivial, but I can't find an argument, why the orthochronal transformations (i.e. those for which \Lambda^0{}_0 \geq 1) form a subgroup of the Lorentz group, i.e. why the product of two orthochronal transformations is again orthochronal? Since when you multiply two...

Homework Statement Verify that (2.16) follows from (2.14). Here \Lambda is a Lorentz transformation matrix, U is a unitary operator, M is a generator of the Lorentz group. Homework Equations 2.8: \delta\omega_{\rho\sigma}=-\delta\omega_{\sigma\rho} M^{\mu\nu}=-M^{\nu\mu} 2.14...

Homework Statement i) Show that the Lorentz group has representations on any space \mathbb{R}^d for any d = 4n with n = 0, 1, 2, . . .. Show that those with n > 1 are not irreducible. (Hint: here it might be useful to work with tensors in index notation and to think of symmetry...

Why the six generator of the restrict lorentz group are the three rotation's generator(angular momentum) and the three boost's generator?

I'm very very very confused and extremely thick. If \Lambda_i is some element of the Lorentz group and \Lambda_j is another, different element of the group then under multiplication... \Lambda_i \Lambda_j is also an element of the Lorentz group, say \Lambda_i \Lambda_j...

What role does the Lorentz Group play in the General Relativity ?

I read that the generator of the O(3) group is the angular momentum L and that the generator of the SU(2) group is spin S. Nevertheless I have some questions. 1. In some books they say that the generator of the SO(3) group is angular momentum L. SO(3) is the group of proper rotations...

What is the rotation transformation generator? What is the Lorentz group generator?

Dear all, I just received by mail the https://www.amazon.com/dp/0471925675/?tag=pfamazon01-20. I am very very happy. At each page I can see something new to learn. But I would like to learn a bit more about his remark on page 28. (you can read it with the amazon reader) He talks about...

Hello everyone, In wikipedia when searching Lorentz representations, there is given that (1/2,0)*(0,1/2) corresponds to Dirac spinor representation and (1/2,1/2) is vector representation, but in P.Ramond's book "Field Theory - A Modern Primer" I read (1/2,0)*(0,1/2)=(1/2,1/2), obviously I...

Is Lorentz group correct?, my question is let's be a group A so the Lorentz Groups is a subgroups of it so A>L (L=Lorentz group , G= Galilean group) of course if we had an element tending to 0 so: A(\hbar)\rightarrow L (Group contraction) so for small h the groups A and L are the same and...