# 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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### Wave function - Dirac Notation

Based on that notes (equation 54): https://warwick.ac.uk/fac/sci/physics/staff/academic/boyd/stuff/dirac.pdf I was reading about the wave functions and I have a question about the notation. You can ...
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### What spinor field corresponds to a forwards moving positron?

When we search for spinor solutions to the Dirac equation, we consider the 'positive' and 'negative' frequency ansatzes $$u(p)\, e^{-ip\cdot x} \quad \text{and} \quad v(p)\, e^{ip\cdot x} \,,$$ ...
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### Sign of energy and frequency in a propagation amplitude

The following paragraph is from pag. 55 of Peskin and Schroeder's An Introduction to Quantum Field Theory: First consider the propagation amplitude $\langle 0|\psi(x) \bar{\psi}(y)|0 \rangle$, ...
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### What is the meaning of $\not{p}$ in physics?

I am reading Srednicki's QFT book in physics. On page 286, the formula $(45.16)$ has a notation $\not{p}$. What is the meaning of $\not{p}$ in physics? Thank you very much.
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### Weyl and Majorana-Weyl spinors why need commutation?

Let $\psi$ denote a Dirac spinor then Weyl spinors are defined by: $$\psi_{L,R}=\frac{1}{2} (I\pm \gamma)\psi$$ on even dimensions $\gamma$ commutes with $\sigma_{\mu \nu}$ (generators used to define ...
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### What's the path of least action for fermions off-shell?

The Lagrangian of fermions is first order both in space-derivatives and time-derivatives. In the variation of the action one usually fixes both the initial point and end point. I have the following ...
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### Is a (Dirac) Particle Where $\vec{p} = (p^1,0,0)$ in an Eigenstate of Helicity? [closed]

Is a particle where $\vec{p} = (p^1,0,0)$ an eigenstate of the helicity operator? First, can I determine this without doing the math? Second, I also wanna prove it mathematically but doing the math ...
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### Hermiticity of Dirac Operator $\gamma^{\mu}D_{\mu}$ and Expansion in eigenmodes

I'm interested to know under what conditions $\gamma^{\mu}D_{\mu}$ is a hermitian operator. I am studying the Fujikawa method of anomalies and I see that many sources have different answers for this. ...
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### Antiparticle solution of the Dirac Equation

I'm really confused by the antiparticle solution of the Dirac equation. I follow Chapter 11 of Schwartz's book "Quantum Field Theory and the Standard Model" and find a couple of problems. In ...
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### Weyl transformation of Dirac equation

The Dirac Equation is given by $$\left(i\gamma^\mu\partial_\mu- \frac{mc}{\hbar}\right)\Psi_D = 0,$$ where $\gamma^\mu$ are the Dirac $\gamma$-matrices and $\Psi_D$ is a Dirac spinor. I would like to ...
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### Dirac Fields and Derivatives (Am I gaining extra minus signs?)

I've given myself a severe headache jumping between East/West Coast sign conventions; I have picked up an extra minus sign and could do with a hand. I am currently using $\eta=\textrm{Diag}[-,+,+,+]$ ...
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### Relation between spinors and anticommutation relation of fermions

I read that the state of a pair of particles is the tensor product of the single states of both, and you will get a wavefunction with the parameters of both, if you swap the parameters you will get a ...
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### Which one is more fundamental in nature: matter or radiation?

I am following a geometric perspective on abelian gauge theory as done in the lecture notes by Timo Weigand, chapter 6, pp 165-167, here: http://www.thphys.uni-heidelberg.de/~weigand/QFT1-13-14/...
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### Do the equations of motion simply tell us which degrees of freedom are superfluous?

A massless spin $1$ particle in 4D has 2 degrees of freedom. However, we usually describe it using four-vectors, which have four components. Hence, somehow we must get rid of the superfluous degrees ...
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### Electromagnetic Dirac equation in CGS units

The Hamiltonian of the Dirac equation in with an electromagnetic field in SI units is $$H=\gamma^0\left[ mc^2+c\gamma^k\left( p_k-\frac{q}{c}A_k \right) \right]+qA^0$$ (from https://en.wikipedia.org/...
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### Formal definition of gauge field and spinors in QFT

I am trying to pin down what spaces a spinor and gluon gauge field exactly occupy. I know that the spinor is a quantity $\psi_{i\alpha f}(\vec x, t)$ where $i$ is a color index in the fundamental ...
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### expanding a Dirac spinor in Weyl basis

For a massless electron Dirac spinor in Weyl basis (where $\chi$ is the left-handed spinor and $\eta$ is the right-handed spinor): \begin{pmatrix} \chi \\ \eta \end{pmatrix} \end{...