I'd like to know how to solve the dirac equation with some small gauge potential $\epsilon \gamma^\mu{A}_\mu(x)$ by applying perturbation theory. The equations reads as $$(\gamma^\mu\partial_\mu-m+\epsilon\gamma^\mu A_\mu(x))\psi(x) = 0.$$
The solution up to first order is
$$ \psi(x) =...
Hello,
I read that satellites is effected by the time dilation caused by gravity and also by that one from special relativity. And so there is a need to prepare the onboard clock to ensure that the time is synchronized with a clock on Earth.
But why is this effect not symmetric? The...
Hello,
I know QED and QCD as isolated theories but now I thought about particle interactions with QED and QCD processes (like fpr proton-antiproton scattering). But I'm not sure how to interpret this mathematically.
As I understood my Feynman diagrams are nothing more like pictures for the...
Thanks. So the eigenvalues of this operators are real?
But shouldn't the hermitian operators \psi + \psi^\dagger and i(\psi - \psi^\dagger) you gave, satisfy the commutation relations if and only if \psi, \psi^\dagger satisfy the anti-commutation relations?
So the only possibility to get hermitian operators are the number-operators? But could the Lagrangian (it should also be hermitian) be rewriten in terms of number-operators?
Hello,
I'm a bit confused about the eigenvalues of the second quantized fermionic field operators \psi(x)_a. Since these operators satisfy the condition \{\psi(x)_a, \psi(y)_b\} = 0 the eigenvalues should also anti-commute? Does this mean that the eigenvalues of \psi(x)_a are...
It should be [\overline{\psi}_a, \psi^a] := \sum_a \overline{\psi}_a \cdot \psi^a - \psi^a \cdot \overline{\psi}_a..
To ensure that the Lagrangian is hermitian we may add an aditional four divergence.
Hello,
I need some help to find the correct symmetrized Lagrangian for the field operators. After some work I guess that
$$\mathcal{L} = i[\overline{\psi}_a,({\partial_\mu}\gamma^\mu \psi)^a] -m[\overline{\psi}_a,\psi^a ]$$
should be the correct Lagrangian but I'm not sure with this.
I'm...
Thanks for your answers. The fact that the operator should be self-adjoint makes sense but there is one problem left.
If we assume that all the operators are self-adjoint and not defined everywhere (since they are unbounded) how can we make sure that the products of operators are...
Hi Guys,
at the moment I got a bit confused about the notation in some QM textbooks. Some say the operators should be symmetric, some say they should be self-adjoint (or in many cases hermitian what maybe means symmetric or maybe self-adjoint). Which condition do we need for our observables...
At the moment I'm working with the https://en.wikipedia.org/wiki/Schwinger's_quantum_action_principle']quantum[/PLAIN] action principle of J. Schwinger. For this I read several paper and books (like: Quantum kinematics and dynamics by J. Schwinger, Schwinger's Quantum action principle by K.A...
I can rewrite the Lagrangian in a form where a new field $\sigma$ appears and for this field exists no kinetic term. I thougth this means that there are no external lines for this field. So is there a link between this kinetic term and the external lines?
And how is it possible that we obtain...
Hello,
Consider the the following Lagrangian of the $\phi ^4$ theory:
$$\begin{align*} \mathcal{L} = \frac{1}{2} [\partial ^{\mu} \phi \partial _{\mu} \phi - m^2 \phi ^2] - \frac{\lambda}{4!} \phi ^4 \end{align*}$$
Now I'm interested in Feynman diagrams.
1. The second term gives the...