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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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You may use one of representations, then - prove the relation $\gamma_{\mu}^{+} = \gamma_{0}\gamma_{\mu}\gamma_{0}$ in this representation, and finally prove that it is correctly for an arbitrary repr …
answered Feb 7 '14 by Andrew McAddams
2
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1answer
Let's have two forms of Majorana equation. First form (standart or spinor representations of gamma-matrices). $$ i\gamma^{\mu} \partial_{\mu}\Psi - m\Psi = 0, \quad \Psi = \Psi_{c} = \hat {C} \bar …
asked Feb 4 '14 by Andrew McAddams
2
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0answers
The Dirac equation may be interpreted as the action of projection operator $\frac{1 - \Delta}{2}\Psi = 0$, where $$ \Delta = \begin{pmatrix} 0 & \Delta_{b \dot {a}} \\ \Delta^{\dot {b}a} & 0 \end{pm …
asked Feb 20 '14 by Andrew McAddams
3
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It's convenient to rewrite EH action in terms of spin connection. From its definition $$ \omega^{\mu}_{ab} = e^{\nu}_{a}\partial^{\mu}e_{\nu b} - \Gamma^{\mu}_{\lambda \sigma} e_{a}^{\lambda}e_{b}^{\s …
answered Jan 10 '15 by Andrew McAddams
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Let's have the spherical spinors $\psi_{j, m, l = j \pm \frac{1}{2}}$, $$ Y_{j, m, l = j \pm \frac{1}{2}} = \frac{1}{\sqrt{2l + 1}}\begin{pmatrix} \pm \sqrt{l \pm m +\frac{1}{2}}Y_{l, m - \frac{1}{2}} …
asked Feb 27 '14 by Andrew McAddams
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There is some little historical reference. The Dirac equation has two linearly solutions which are the eigenstates of Dirac hamiltonian: first refers to the positive values of energy while the second …
answered Mar 9 '14 by Andrew McAddams
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0answers
Recently I get the task to build (2 + 1)-Dirac theory. I wrote corresponding Dirac equation in a form $$ (i\sigma_{0}\partial_{0} + i\sigma_{1}\partial_{1} + i\sigma_{2}\partial_{2} - m)\Psi = 0, $$ w …
asked Mar 4 '14 by Andrew McAddams
1
vote
2answers
Let's have Schrodinger equation or Dirac equation in Schrodinger form: $$ i \partial_{0}\Psi = \hat {H}\Psi . $$ Sometimes we can introduce some operators $\hat {A}, \hat {B}$ (the second is not alway …
asked Oct 29 '13 by Andrew McAddams
1
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0answers
Let's have arbitrary half-integer spin $n + \frac{1}{2}$ representation: $$ \Psi_{\mu_{1}...\mu_{n}} = \begin{pmatrix} \psi_{a, \mu_{1}...\mu_{n}} \\ \kappa^{\dot {a}}_{\quad \mu_{1}...\mu_{n}}\end{pm …
asked Mar 28 '14 by Andrew McAddams
10
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1answer
I have a few questions about Majorana fermions. What is Majorana mass? Does it have a different value compared to the mass in the Dirac equation for an arbitrary fermion? How exactly do they differ? …
asked Nov 20 '13 by Andrew McAddams
2
votes
1answer
Recently I heard that there is some "alternate" equation for the Dirac one. It can be introduced if we refuse some properties of the theory describes the electron, which Dirac used in his original art …
asked Nov 19 '13 by Andrew McAddams
3
votes
1answer
In first order of perturbation theory the S-matrix amplitude for electron scattering in the Coulomb field will be (up to normalization factors) $$ S_{fi} = \frac{iZ q^2}{\sqrt{2E_{f}2E_{i}}}\bar {u}(p …
asked Mar 13 '14 by Andrew McAddams
3
votes
1answer
I tried to check the statement that Dirac free Hamiltonian commutes with inversion operator. For $$ \hat {P}\Psi(\mathbf r , t) = i\hat {\gamma}_{0}\Psi (-\mathbf r , t), \quad \hat {H} = (\hat {\alph …
asked Mar 3 '14 by Andrew McAddams
2
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0answers
Here I asked about getting an equation for two-component spinor as the alternative for Dirac equation. It was found that it is called Majorana equation. It may be easily derived by using historical Di …
asked Nov 24 '13 by Andrew McAddams
2
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Here is one tricky way to show that the Dirac representation is invariant under C,P,T-transformations. The free Dirac theory refers to the direct sum $\left( 0 , \frac{1}{2}\right) \oplus \left( \frac …
answered Jul 26 '14 by Andrew McAddams

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