Recent content by Neutrinos02

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?

But isn't there a self-adjoint extension with generalized eigenstates like for the QM operators x,p ?

No, but the eigenvalues are not matrices? And in the path integral formalism we use Grassmann valued fields.

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...