All Questions
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Is the Dirac adjoint in the representation dual to Dirac spinor?
As seen in this Wikipedia page, the Lorentz group is not compact and the Dirac spinor (spin $\frac{1}{2}$) representation is NOT unitary.
Therefore, the complex conjugate representation does NOT ...
- 1,669
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Trying to solve the energy levels of a spin 1/2 particle in a one-dimensional box using Dirac Equation
I was studying the problem I asked above in the title and found the article P Alberto et al 1996 Eur. J. Phys. 17 19.
The wave function inside the walls is:
$$
\psi(z)=B\ exp(ikz) \left[\begin{array}{...
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How to motivate spinors from the Dirac equation? [closed]
I am trying to motivate spinors by making sure the Dirac equation is relativistically invariant (and it suffices to discuss just the Dirac operator).
Let $\{ e_i \}$ be an orthonormal frame and $x^i$ ...
- 498
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Interpretation of "spin-1/2" in classical Dirac field
I emphasize that the proceeding is purely classical physics. Consider the Grassmann-valued field (where $\mathcal{N}$ is a Grassmann number), which is a solution to the Dirac equation, given by
$$\psi(...
- 2,676
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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 ...
- 1,783
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Wavefunction spinor in Dirac equation
Which is the physical interpretation that in Dirac's equation the wavefunction is a spinor?
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561
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Bilinear covariants of Dirac field
In the book "Advanced quantum mechanics" by Sakurai there is a section (3.5) about bilinear covariants, however i can't really find a definition of these objects, neither in the book nor ...
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3
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What are Dirac spinors and why did relativistic quantum mechanics need them?
I have a good grasp of the Schrödinger equation and the basics of special relativity But the Dirac equation is alien to me. What are Dirac spinors and why did Dirac use them?
user353451
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What does quantization of spin have to do with spinors?
A fermion has half-integer spin. In the context of the theory, this means its wavefunction is made of spinors: geometric objects which, under Lorentz rotations, transform in such a way that they ...
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What is the relationship between spinors and rotating motion geometrically?
Spinors are famously like spinning tops, but not actually like spinning tops since they are point particles and thus cannot rotate around their axis. It is easy to show algebraically how spinors must ...
- 133
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Lorentz boost property of gamma matrices
I was watching this video where he boosted the Dirac equation. He reached this equation:
$$S^{-1}(\Lambda)\gamma^\mu S(\Lambda)=\Lambda^\mu{}_\nu \gamma^\nu$$
My question is since $\gamma^\mu$ is a ...
- 1,324
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146
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Angular-momentum of the Dirac spinor theory
The standard Dirac action
$$
S = \int d^4 x \bar \psi (i \gamma^\mu \partial_\mu - m) \psi
$$
is invariant under Lorentz transformation.
In David Tong's lecture note, eq (4.96) lists that the ...
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Quantum Field Theory Unitary Transformations
I am currently reading through Itzyskon and Zuber for my quantum field theory class, and I came across this regarding the unitary transformations of the Dirac bispinors in chapter 2. They show that ...
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2
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To construct a Lorentz scalar we use $\psi^{\dagger}\gamma^{0}\psi$. Could we use $\gamma^{5}$ instead of $\gamma^{0}$ seen as both are Hermitian?
Both $\gamma^{0}$ and $\gamma^{5}$ are Hermitian, so could we replace $\gamma^{0}$ with $\gamma^{5}$ to construct a Lorentz scalar with the same properties as $\bar{\psi}\psi$?
- 115
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Dirac spinor in the chiral basis
In the chiral basis, the gamma matrices take the form
$$
\gamma^0=\begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}, \quad \gamma^j=\begin{bmatrix}0 & -\sigma^j \\ \sigma^j & 0\end{bmatrix}
$$...
