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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How does special relativity lead to anti-particles?

Anti-particles and spinors pop out of the Dirac equation very naturally, yet the Dirac equation is only a modified version of the Schrödinger equation which includes the relativistic energy-momentum ...
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Relation between four-components of the Dirac wavefunction and the four solutions of the Dirac equation

Recently I've been studying the Dirac equation. I've studied that the Dirac wavefunction must have four components ($4\times 1$ column matrix) since the Dirac Hamiltonian must be a $4\times4$ matrix ...
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Transition from positive energies to negative energies in Dirac equation

In textbooks, the criticism of the Dirac equation is that it may allow transitions from the positive energy state $m c^2$ to its corresponding negative energy state by releasing one or more photons. ...
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How to derive this form of helicity spinor (massless/high energy limit)

Srednicki 50.7 says that in the massless limit, we can express $$u_-(\textbf{p})\bar{u}_-(\textbf{p}) = \begin{pmatrix} 0&-p_{a\dot{a}}\\0&0\end{pmatrix}$$ This comes from a previously ...
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The dimension of the Clifford algebra for the Dirac equation

The Dirac algebra contains sixteen linearly independent elements. In general, a Clifford algebra $\mathcal{C}\!\ell(V,Q)$ generated from a vector space $V$ equipped with a quadratic form $Q$ has ...
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Obtaining the 16 elements of the Clifford algebra from the $\gamma^\mu$ generators

In my study of the Dirac equation, I have fully understood the "linearization" of the relativistic energy to obtain a matrix-valued equation that reduces to the Klein-Gordon equation if the ...
1 vote
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Charge conjugation is a symmetry for the quantized free Dirac action?

I am self-studying QFT on "A modern introduction to quantum filed theory" by Maggiore, and on page 95 he states: "For the free Dirac action, one immediately sees that C,P and T are ...
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Electrostatic potential created by a relativistic bounded electron (i.e a 4-spinor)

Let's take the Gordon solution of the central field Dirac equation for the Hydrogen atom and look at the wave functions. There is bounded functions inside the spinor, which represents here the full ...
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Why is the derivative necessary to connect left and right-hand spinors?

I am studying Weyl and Dirac spinors. Suppose we have two Weyl fermions $\eta, \chi$ transforming under $(1/2,0)$ representation of the Lorentz group. I learned that to construct Lorentz invariant ...
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What is the difference between a twistor and bispinor?

Reading the book on General Relativity written by R.M. Wald I (tags according to Wald's book) encountered the concept of a twistor $$Z = (\omega^A, \pi_{A'}) \tag{14.1.9}$$ which looks very much as ...
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Calculating time dilation from a solution to the Dirac equation

Suppose I have a Muon in a potential well. Its wavefunction is a solution of the Dirac equation, a relativistic version of the Schrodinger equation for spin 1/2 particles. Because the particle is &...
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Obscure Calculations in Foldy-Wouthuysen Transformation (electron in EM field)

I'm studying the Foldy-Wouthuysen Transformation on Bjorken-Drell's book and I got stuck strying to replicate some calculations. First of all, introducing the transformation $\psi'=e^{iS}\psi$ we get ...
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The Dirac-Hestenes equation as an eigenvalue equation: Interpretation of the $m \psi \gamma_0$ term and the wavevector

This is somewhat of a follow-up question to my previous question on the Dirac-Hestenes equation. In that question, I asked whether the equation could be written in a form that omits the dangling ...
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Product of Dirac $\gamma^0$ and $\gamma^\mu$ generate a representation of some algebra?

I need your help with an issue about Dirac gamma matrices. Precisely, I need to know if $\gamma^0\gamma^\mu$ generates an irreducible representation of some algebra. This problem has come out in the ...
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I would very much like to understand the motivation behind the correlation between: $(i\partial\!\!/-eA\!\!/-m)\psi=0$ and $(i\partial\!\!/+eA\!\!/-m)\psi_c=0$ when dealing with the derivation of the ...