1. ### A Getting particle/antiparticle solutions from the Dirac Equation

Hi! I am studying Dirac's equation and I already have understood the derivation. Following Griffiths, from factoring Einstein's energy relation with the gamma matrices: ## (\gamma^\mu p_\mu + m)(\gamma^\mu p_\mu - m) = 0 ## You take any of the two factors, apply quantization and you arrive to...

4. ### I Relativistic quantum mechanics

Given that the Minkowski metric implies the Lorentz transformations and special relativity, why do the equations of relativistic quantum mechanics, i.e., the Dirac and Klein-Gordon equations, require a mass term to unite quantum mechanics and special relativity? Shouldn't their formulation in...

10. ### Understanding solutions of Dirac equation

some notes: There was actually no proof given why ##u^s(p)## or ##v^s(p)## should solve the Dirac equation, only a statement that one could prove it using the identity $$(\sigma\cdot p)(\bar\sigma\cdot p)=p^2=m^2.$$ We were using the Wely-representation of the ##\gamma##-matrices, if this should...
11. ### Calculating field transformation

Homework Statement Let ##\psi(x)=u(p)e^{-ipx}##, where $$u((m,0)) = \sqrt{m}\begin{pmatrix} \xi\\\xi \end{pmatrix}\quad\text{where}\quad \xi = \sum_{s\in \{+,-\}}c_s\xi^s\quad \text{and}\quad \xi^+\equiv\begin{pmatrix} 1\\ 0 \end{pmatrix}\quad \xi^-\equiv\begin{pmatrix} 0\\ 1 \end{pmatrix},$$...

23. ### A The Lagrangian Density and Equations of Motion

Can Lagrangian densities be constructed from the physics and then derive equations of motion from them? As it seems now, from my reading and a course I took, that the equations of motion are known (i.e. the Klein-Gordon and Dirac Equation) and then from them the Lagrangian density can be...
24. M

### Breit Interactions

I am finding references and good books for the conceptual understanding of Breit Interactions. Are there any books which specifically include the topic? The related topics explaining the formulation Breit Hamiltonian and its involvement to the correction to the atomic structure calculation are...
25. ### A How the g factor comes from QFT?

I'm reading the book Quantum Field Theory and the Standard Model by Matthew Schwartz and currently I'm studying the chapter 17 titled "The anomalous magnetic moment" which is devoted to computing the corrections due to QFT to the g factor. My main issue is in the begining of the chapter, where...
26. ### B The Dirac equation and the spectrum of the hydrogen atom

I was reading that one of the successes of the Dirac equation was that it was able to account for the fine structure of some of the differences in the spectrum of the hydrogen atom. But the Dirac equation is about subatomic particles moving at relativistic velocities. But an electron around the...
27. ### Dirac Lagrangian invariance under chiral transformation

Consider the Dirac Lagrangian, L =\overline{\psi}\left(i\gamma^{\mu}\partial_{\mu}-m\right)\psi, where \overline{\psi}=\psi^{\dagger}\gamma^{0} , and show that, for \alpha\in\mathbb{R} and in the limit m\rightarrow0 , it is invariant under the chiral transformation...
28. ### I How is Graphene's Hamiltonian rotationally invariant?

Graphene's Hamiltonian contains first order derivatives (from the momentum operators) which aren't invariant under simple spatial rotations. So it initially appears to me that it isn't invariant under rotation. From reading around I see that we also have to perform a rotation on the Pauli...