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Tagged with special-relativity spinors
212
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Split Pauli Four-vector as quadratic terms of spinors
If I have the Pauli Four-vector $$x_{\mu}\sigma^{\mu} = \left(\begin{array}{cc}
t+z & x-i y \\
x+i y & t-z
\end{array}\right)$$ with $\sigma^0$ as Identity Matrix. Is there some way to write ...
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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 ...
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Schwichtenberg Physics from Symmetry p. 83 Eq 3.225
Firstly - an apology. This is my first question to Stack Exchange and also my first attempt at using Latex. I need to show a subscript letter with a dot above it, but can't work out how to do that ...
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How is the complexification of the Lorentz Lie algebra related to the need for Dirac's 4-component spinor in QFT?
There have been several questions with good answers in physics.stackexchange about the motivation of the complexification of the Lorentz Lie algebra, basically as a mathematically nice way to deal ...
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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:
$$
\psi(z)=B\ exp(ikz) \left[\begin{array}{...
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How to motivate spinors from the Dirac equation? [closed]
I am trying to motivate spinors by making sure the Dirac equation is relativistically invariant (and it suffices to discuss just the Dirac operator).
Let $\{ e_i \}$ be an orthonormal frame and $x^i$ ...
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What is the connection between Lorentz transforms on spinors and vectors?
When deriving the (1/2,0) and (0,1/2) representations of the Lorentz group one usually starts by describing how points in Minkowski space transform while preserving the speed of light (or the metric).
...
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Building 4-vectors out of Weyl spinors: Combining 2 independent Weyl spinors and a sigma matrix to get a 4-vector
i'm struggling with this problem
In Exercise 2.3 of A Modern Introduction to Quantum Field Theory of Michele Maggiore I am asked to show that, if $\xi_R$ and $\psi_R$ are right-handed spinors, then
$$...
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1
answer
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Transformation between left-handed spinors and right-handed spinors
I am learning (Weyl) spinor formalism from Müller-Kirsten and Wiedemann's Introduction to Supersymmetry (2nd Ed., WS, 2010, here). I am quite confused about the transformation between left-handed ...
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Can we make a Bloch sphere for Weyl spinors?
If spinors are the "square root" of 3-vectors [$\mathrm{SU}(2)$ double cover of $\mathrm{SO}(3)$], Weyl spinors can be thought of as the "square root" of 4-vectors [$\mathrm{SL}(2,\...
- 207k
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Does the Dirac Spinor live in the complexification of the Lorentz group?
In this question I learned that when working with quaternionic representations of (the double cover of) our relevant orthogonal group, we cannot avoid working in complex vector spaces. However it is ...
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1
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Lorentz Invariance of Weyl Lagrangian
I have been reading 'Quantum Field Theory and the Standard Model' by Schwartz and have gotten stuck on a line of reasoning in Section 10.2.2.
I understand that we can construct a (right-handed) four-...
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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(...
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Weyl spinors under the Lorentz transformation
I am reading An Modern Introduction to Quantum Field Theory by Maggiore. On page 28, it says
Using the property of the Pauli matrices $\sigma^2 \sigma^i \sigma^2 = -\sigma^{i*}$ and the explicit form ...
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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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