Questions tagged [anticommutator]
The anticommutator tag has no usage guidance.
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Are there any 3 or more Hermitian solutions to the problem: $\alpha_i^2=1$, $\{\alpha_i, \alpha_j \}=2$
I’m trying to generate some matrices which are similar to Pauli’s but with the following anti-commutation relation
$$\{\alpha_i, \alpha_j\}=\alpha_i \alpha_j + \alpha_j \alpha_i = 2 \tag{1}$$
And
$$\...
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Commuting but not anti-commuting operators
Two Hermitian operators $\hat{A}$ and $\hat{B}$ are such that they commute but don't anti-commute. In this case, even they commute their uncertainty product will not be zero, is it right?
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Derivation of anti-commutation relations of massive supermultiplet generators [closed]
In almost all intro to supersymmetry notes the commutation relations are given between the generators and their conjugates however, I can not find any proofs of them anywhere and am struggling to ...
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Defining particles by their commutation/anti-commutation relations
In my studies of many-body physics, I have encountered three types of particles, which can be defined based on their commutation/anti-commutation relations.
Fermions, defined by raising/lowering ...
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Right derivative of Grassmann number and associated anti-commutation relation
I am reading chapter 3 of Anomalies in quantum field theory by Reinhold Bertlmann and I found one statement that I don't know how to prove. First of all he defined the right derivative on the ...
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On the normal ordering of Fermi fields
From my understanding, the normal ordering of Klein-Gordon fields in QFT is valid because of the ambiguity that comes with quantizing a classical theory, in the sense that the conmutator of fields is ...
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Pauli Exclusion Princple for a fermion and antifermion
I understand that the Pauli Exclusion Principle applies only for identical particles, so that a fermion and an anti-fermion should be allowed to be in the same state. However, when I look at the ...
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Anti-commutator of Dirac matrices
Consider $$ \beta = \begin{pmatrix} \mathbf{1} & 0 \\ 0 & -\mathbf{1} \end{pmatrix},\quad \alpha_i = \begin{pmatrix} 0 & \mathbf{\sigma}_i \\ \mathbf{\sigma}_i&0 \end{pmatrix}.$$ The ...
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(Anti)commutation of creation and annhilation operators for different fermion fields
The Fourier expansion of the fermion field operator is such that
$$ \hat\psi=\int\!d^3p\,\left[ f_b(p)\hat b(p) +f_d(p)\hat d^\dagger\!(p) \right] ~~, $$
for some sufficiently complicated $f_b$ and $...
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Measurements, QFT and Wightman's axiom 3
I think I might have misconceptions about the conceptual core of QFT. Let me explain where I am puzzled.
In QM, the measurement process is accounted by the postulate of collapse of the wave function: ...
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Show $[\gamma^\mu,\eta^{\nu\lambda}I]=0$ for Dirac matrices
I am trying to show the following commutation relation for the Dirac matrices $\gamma^\mu$ and the metric $\eta^{\nu\lambda}$: $$2[\gamma^\mu,\eta^{\nu\lambda}I]=0$$
where $I$ is the 4x4 identity ...
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What is a fermionic field theory?
Let $\mathscr{H}$ be a Hilbert space and $\mathscr{H}^{n}$ be the associated $n$-fold tensor product of this Hilbert space. I'll skip the mathematical details in what follows, but my approach follows ...
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Why is the anti-commutation relation $\lbrace \psi_a(x), \bar{\psi}_b(y) \rbrace = 0$ enough to ensure causality?
In quantum field theory, it is crutial that two experiments can not effect each other at space-like seperation. Thus $[\mathcal{O}_1(x), \mathcal{O}_2(y)] = 0 $ if $(x-y)^2 < 0$.
For the Klein-...
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Why is the anticommutator of the uncertainty principle omitted if it serves to increase the accuracy of our "knowledge" of a quantum state?
The generalized uncertainty principle can be derived and shown to be this which is fine and rigorous.
$\langle ( \Delta A )^{2} \rangle \langle ( \Delta B )^{2} \rangle \geq \dfrac{1}{4} \vert \langle ...
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How to express the anti-commutator in the form of a density operator?
$
\newcommand{\ket}[1]{|{#1}\rangle}
\newcommand{\bra}[1]{\langle{#1}|}
\newcommand{\braket}[2]{\langle{#1}|{#2}\rangle}
\newcommand{\acomm}[2]{\left\{#1,#2\right\}}
$Let $\{ \ket{1} \ket{1} \ket{2} .....
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