# Questions tagged [anticommutator]

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### Is there a Stone-von-Neumann theorem-like result for the canonical anti-commutation relations (CAR)?

The canonical commutation relation (CCR) $$[\phi(x), \pi(y)] = i\hbar\delta(x-y)$$ is kind of the key to basically any bosonic quantum theory. This is due to many different remarkable properties: By ...
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### Which of these commutation relations are correct? [closed]

I saw, in two different references, the following two commutation relations for the fermionic field operator: and which one of them is correct? 1 "Stefanucci, Gianluca, and Robert Van Leeuwen. ...
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### Anticommutation and Bogoliubove transformation

I am given the following transformation: \begin{bmatrix} ...
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### Anticommutator of Fourier transform

Let $$a_x = \int_{-\pi}^\pi \frac{\text{d}q}{2\pi}e^{iqx}a(q)$$ $$a_x^\dagger = \int_{-\pi}^\pi \frac{\text{d}q}{2\pi}e^{-iqx}a^\dagger(q)$$ ...
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### What is the physical meaning of the anticommutator of two observables? [duplicate]

It is quite clear to me that when two operators commute it implies that two different observables associated with the respective operators can be measured simultaneously with the exact accuracy. But ...
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### Spinor index, dirac field equation

Sometimes I read anticommute $$\{\psi(x),\psi^\dagger(y)\}=\delta^{(3)}(x-y)$$ Sometimes, $$\{\psi_a(x),\psi_b^\dagger(y)\}=\delta^{(3)}(x-y)\delta_{ab}$$ Are they the same, second one just emphasis ...
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### Creation and annihilation operators for fermions from anticommutator

In a question, I was given that $a^{\dagger}a + a a^{\dagger} =1$ and asked to show what $a|n\rangle$ and $a^{\dagger}|n\rangle$ would be, given that $H|n\rangle=(a^{\dagger}a + 1/2)$. I am getting ...
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### (Anti)commutators at different times

Why does the commutator of two operators evaluated at different times vanish? Take for instance a fermonic field $\psi_\sigma (\vec{x},t)$, which satisfies the well known anti-commutation relations ...
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1 vote
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### Anticommutator of gauge covariant derivatives

I must convert some dimension-6 operators I've obtained to the SILH base (ref: this, "Review of the SILH basis", CERN presentation by R. Contino). In this conversion I've got operators such ...
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Can we simplify $$Σ_s Σ_r [b_p^s u^s(p)\mathrm e^{ipx} (b_q^r)^†(u^r)^†(q)\mathrm e^{-iqy} + (b_q^r)^†(u^r)^†(q)\mathrm e^{-iqy} b_p^s u^s(p)\mathrm e^{ipx}]\tag{1}$$ as $$Σ_sΣ_r[ \{b_p^s, (b_q^r)^†... • 349 0 votes 0 answers 245 views ### Anti-commutator in Quantization of Dirac field Can anyone explain while calculating \left \{ \Psi, \Psi^\dagger \right \} , set of equation 5.4 in david tong notes lead us to$$Σ_s Σ_r [b_p^s u^s(p)e^{ipx} b_q^r†u^r†(q)e^{-iqy}+ b_q^r †u^r†(q)e^{...
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Define $$M_{\theta} \equiv \exp\left[\theta \sum_s \left(d^{\dagger}(\vec{p},s)b(\vec{p},s) -b^{\dagger}(\vec{p},s)d(\vec{p},s)\right)\right],$$ where $\theta$ is a continuous real parameter. Show via ...