Hi,
I would like to understand the left-invariant vector field of the additive group of real number. The left translation are defined by
\begin{equation}
L_a : x \mapsto x + a \; , \;\;\; x,a \in G \subseteq \mathbb{R}.
\end{equation}
The differential map is
\begin{equation}
L_{a*} =...
Hi VoxCaelum, my previous reply was not directed towards you. I will look into your answer and come back if I have any questions. Thanks for your reply.
Hi,
I am having trouble following the Peskin and Schroeder and their derivations to show that a Dirac particle is a spin 1/2 particle (page 60 and 61). I understand how he gets the first (unnumbered) equation on page 61. However, I don't understand how he gets to the second equation...
But if $\phi$ is an eigenfunction of $\psi$, then:
\begin{equation}
\langle \phi | \psi \rangle
\end{equation}
is the transition amplitude, right? (I think that is maybe what the OP is asking.)
Hi,
In QFT we define the projection operators:
\begin{equation}
P_{\pm} = \frac{1}{2} ( 1 \pm \gamma^5)
\end{equation}
and define the left- and right-handed parts of the Dirac spinor as:
\begin{align}
\psi_R & = P_+ \psi \\
\psi_L & = P_- \psi
\end{align}
I was wondering if the left- and...
Unfortunately my German is not as good as I wish it was so I can't read the article. I think you are right that the factor of 2 is not important for the final (conceptual) result, but these kind of things really annoy me for some reason. And I'm happy I asked this question on this forum, because...
Hmmm... that is very interesting. So you don't think my calculations are wrong, but that the author just adds a total divergence term to influence the expression for the canonical momentum. I never realized that this was allowed and makes me rethink the idea of canonical momentum, because...
Hi,
I'm reading www.phys.ethz.ch/~babis/Teaching/QFTI/qft1.pdf and trying to understand the canonical quantization of the Schrodinger field. In particular, the Lagrangian:
\begin{equation}
\mathcal{L} = \frac{i}{2}\psi^* \partial_0 \psi - \frac{i}{2}\psi \partial_0 \psi^* +...
Hi,
I'm getting a bit confused about the adjoint representation. I learned about Lie algrebras using the book by Howard Georgi (i.e. it is very "physics-like" and we did not distinguish between the abstract approach to group theory and the matrix approach to group theory). He defines the...