# Questions tagged [dirac-equation]

A fully relativistic (Lorentz covariant) description, first put forward by Paul Dirac in 1928, of the first quantized, spin one half fermion with nonzero mass. Physical notions to do with this equation include the Dirac sea, Dirac hole theory, the Klein Paradox and the fine structure of the Hydrogen spectrum.

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### Explain this step (related to gamma matrices and parity operator)

I am having hard time reproducing a step from the textbook "Lecture Notes on Quantum Field Theory", by Ashok Das. On page 429 ( above equation 11.72), the author is talking about the parity ...
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### Wave function fermions and boson, Peskin & Schroeder [closed]

We have, from peskin (the results are right, just citing) the wave function of fermions and bosons, but they have a different sign: Fermions, page 45: Bosons, page 20: The issue here, is that the ...
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### Why Schrodinger equation for graphene electrons is a Dirac equation for massless particles when apparently C atoms & electron cloud aren't massless?

Recently, I was attending in a colloquium and the speaker, quite reputable btw, mentioned shortly that electrons in graphene are governed by Dirac equation instead of Schrodinger equation. However, ...
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### Why do we need the Dirac's hole picture?

When I have to quantize a Dirac field I have to start by the usual classical Lagrangian and find the associated Lagrange equations, then quantize the solutions promoting them to quantum operators. In ...
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### Do $p_\mu$ and $\gamma^\mu$ commute?

So I am trying to derive the relation $\bar{u}_{(s)} (\displaystyle{\not}{p} -m)=0$ from the conjugate dirac equation $(i \partial_\mu\bar{\psi}\gamma^\mu+m\bar\psi) = 0$ but I am running into issue. ...
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### Letting Dirac wave function evolve from an initial wave function

How does one go about calculating the general wave function (which solves the Dirac equation) spanning the entire Minkowski spacetime when only an initial wave function, confined to a constant-time ...
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### Understanding Wave Function Evolution in the Dirac Equation for Different Geometries

I've come to understand that for Schrödinger's equation, you can select an initial wave function within a constant-time space. By allowing it to evolve according to the Schrödinger equation, you can ...
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### Is Dirac neutrino ruled out by current experimental observation?

I have read the neutrino mass problem. The unnatural smallness of neutrino mass implies the existence of new physics so the seesaw mechanism is introduced to solve this theoretical problem. I ...
1 vote
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### Question about a construction of a 1+1 free Dirac field

I have a question about the example Ron Maimon gave here of a (1+1) dimensional free Dirac field. In the original wording: In two dimensions (one space one time), there is a nice dimensionally ...
1 vote
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### Calculation of the source term for the Einstein-Dirac equation in the weak field limit

I have seen the same being done for Einstein- Klein Gordon equations quite successfully. However, I'm struggling with it in the case of the E-D equations. I know that the einstein equations in the ...
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### How the Dirac spinor change under the Lorentz transformation?

My question is, what form do Dirac spinors take under Lorentz transformations? I would be grateful if you could send me the answer this year
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### If a flagpole visualizes a Pauli spinor, what visualizes a Dirac spinor?

@AndrewSteane writes in his textbook that a Pauli spinor is a flagpole - with length, direction, flag orientation - and a sign. A Dirac spinor is a more complicated object. What is the most intuitive ...
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### Dimensional analysis in QFT

I have the Lagrangian density: $$\mathcal{L} = \bar{\psi}(i\gamma^\mu \partial_\mu - M)\psi$$ How do I know what dimensions $\bar{\psi}$ and $\psi$ have?
1 vote
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### Negative energy solutions not a problem for Klein-Gordon equation?

I already posed this question Negative energy solutions in Klein-Gordon and Dirac equations but I am not satisfied with the answers. Trying to be very sharp: does Klein-Gordon equation have negative ...
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### Dirac 4-current for orbital transition

The conserved 4-current is defined as $j^\mu=\bar{\Psi} \gamma^\mu \Psi$ where $\Psi$ is the 4-component wave function. To get the wavefunctions, if we look at the Dirac orbital spinor solution for ...
1 vote
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### Dirac/Weyl/Majorana Basis and their Importance

I have just begun studying Dirac equations and was confused by the physical significance of Dirac Basis. In principle, we can have as many representations of Clifford Algebra as we wish by conducting ...
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### Two normalization constants for Dirac plain wave function

I stumbled across two different expressions for a Dirac plane wave function, namely $$\psi=\sqrt{\frac{m}{EV}}ue^{-ip\cdot x}$$ and $$\psi=\frac{1}{\sqrt{2EV}}ue^{-ip\cdot x}$$ where $u$ is the Dirac ...
1 vote
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### Are the massive spinors (left and right Weyl spinors) helicity eigenstates?

For massless spinor, with the help of Dirac equation, I can show that both left-handed and right-handed Weyl spinors are helicity eigenstates with eigenvalues +1 and -1 (respectively). I am unsure ...
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### Representing the Dirac equation in spacetime algebra without leftover indices

The Dirac equation as derived by Hestenes is $$\hbar \nabla \psi I \sigma_3 = mc \psi \gamma_0$$ where $I \sigma_3 = \gamma_2 \gamma_1$. The equation is claimed to be Lorentz invariant, because the ...