All Questions
7
questions
0
votes
1
answer
68
views
Deducing Lorentz representation out of symmetry type
Cross-posted from here
Lorentz algebra can be proven to be isomorphic to $\mathfrak{su}(2) \oplus \mathfrak{su}(2)$, so every representation can be denoted by two indices or spins, $(j_1, j_2)$.
Let's ...
- 1,597
2
votes
0
answers
308
views
What Lorentz covariance has to do with Lorentz invariance? [duplicate]
Does saying that the Dirac equation is invariant under Lorentz transformations is the same as saying that it is Lorentz covariant?
- 1,045
1
vote
2
answers
798
views
Symmetry under Lorentz transformation: precise definition
I am studying QFT but I need to fill some gaps in my comprehension of special relativity (I didn't study it very well and I know I still misunderstand things in S.R).
In my book it is written:
" A ...
- 1,450
3
votes
3
answers
792
views
Identifying Lorentz Covariant Equations
Statement: $\phi , A^{\mu}, T^{\mu \nu}$ are a Lorentz scalar, vector, and tensor. Which of the following equations are Lorentz covariant.
a. $\phi = A_{0}$
b. $\phi = A^{\mu}A_{\mu}$
c. $\phi = ...
- 131
1
vote
1
answer
170
views
Work out components $F^{01}$ and $F^{ij}$ of the antisymmetric tensor $F^{\mu\nu}$ under the Lorentz Transform [closed]
Work out explicitly how the components $F^{0i}$ and $F^{ij}$ of the antysymmetric tensor $F^{\mu\nu}$ introduced in chapter I.6 transform under a Lorentz transformation
This problem is from Zee, ...
- 163
5
votes
3
answers
5k
views
How to prove a symmetric tensor is indeed a tensor?
Our professor defined a rank $(k,l)$ tensor as something that transforms like a tensor as follows:
$$T^{\mu_1' \mu_2'...\mu_k'}{}_{\nu_1'\nu_2'...\nu_l'} ~=~ \Lambda^{\mu_1'}{}_{\mu_1}...\Lambda^{\...
- 163
2
votes
1
answer
73
views
Testing covariance of an expression?
This is something I've been unsure of for a while but still don't quite get.
How does one tell whether an expression (e.g. the Dirac equation) is covariant or not? I get it for a single tensor, but ...
- 87