Questions tagged [anticommutator]
The anticommutator tag has no usage guidance.
168
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Deriving the equal time anti-commutator of the Dirac fields [closed]
I am trying to solve an exercise on deriving the equal-time anti-commutator of the Dirac fields. But I got stuck somewhere and couldn't get the desired result.
I would like to show that
$$
\{\psi(x), \...
- 41
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$C$-number ignored in charge conjugation
In Weinberg’s QFT V1, under equation 5.5.58, he says that an anticommutator ($c$-number) can be ignored when we exchange spinors, $\psi$ and $\bar{\psi}$. I cannot fully appreciate why we can ignore ...
- 425
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(Anti) Commutation relation of derivative of the fermionic operator
While deriving Semiconductor Bloch equation, I stumbled upon a commutation relation that I have never seen before. It looks like,
$$[\alpha_k^{\dagger}\alpha_k, \alpha_{k'}^{\dagger}(\nabla_{k'}\...
- 1,007
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Does the anticommutator of two spinors affect the transpose of their product?
My lecture notes claim that for an anticommutation relation
$$[ \psi_{\mu}(\bf{x},t),{\psi_{{\nu}}^{*}}(\bf{y},t)] = \delta_{\mu \nu} \delta^3(\bf{x}-\bf{y})$$
between two spinors, the transpose of ...
- 337
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Product of spinors in Dirac field anticommutators
I am reading a "A modern introduction to quantum field theory" by Maggiore and on page 88 it shows the anticommutators of the Dirac field:
$$
\{\psi_a(\vec{x},t),\psi_{b}^{\dagger}(\vec{y},t)...
- 521
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97
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Confusion about whether a fermion field and its conjugate as an Grassmann number
I'm confused about what "a Grassmann-odd number" really means and how does it apply to fermions.
In some text, it says that "if $\varepsilon \eta+\eta \varepsilon =0 $, then $\...
- 368
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How to generalize the (anti)commutation for spacelike separation to more than $2$ field operators?
Let $\phi_1$ and $\phi_2$ be quantum field operators of certain spin on $\mathbb{R}^4$. Then, the principle of locality dictates that if $x$ and $y$ are space-like separated, we have
\begin{equation}
\...
- 1,665
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Geometry of anticommutation relations
I am asking this question as a mathematician trying to understand quantum theory, so please forgive my naivety.
Systems satisfying the canonical commutation relations are naturally modeled with ...
- 45
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Quantization of an Interacting Field Theory
The procedure to quantize free field theories is imposing a commutation/anticommutation relation with the field and its conjugate momentum, as $$\mathcal L = i\bar\psi\gamma^\mu\partial_\mu\psi\...
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Why does $[Q,P]=i\hbar$ work for fermion? Shouldn't fermion satisfy anticommuting relation?
For hydrogen, we use $[Q,P]=i\hbar$ for electron, which is a fermion. Does it have a deeper reason such as that we're really considering the proton + electron system, which might be of bosonic nature?
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Why is commutation bracket used instead of anti-commutation bracket on page 61 of Peskin QFT?
Peskin&Schroeder was performing a trick where they used
$$J_za^{s\dagger}_0|0\rangle=[J_z,a^{s\dagger}_0]|0\rangle\tag{p.61}$$ and claimed that the only non-zero term in this commutator would be ...
- 838
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84
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Help with commutator algebra with fermionic operators
I am struggling to understand how the following is true for the fermionic creation/annihilation operators $a^\dagger, a$: $$[a^\dagger a, a]=-a$$
If someone could walk me through the math derivation ...
- 101
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The renormalized fermionic operators do not anti-commute?
Let's say we have fermionic operators $a$ and $b$ (which anti-commute). In the context of a renormalization scheme (I am thinking specifically of Wilson's NRG, but it could be DMRG) I have a matrix $P$...
- 1,262
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142
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Anticommutation relations for Dirac field at non-equal times
I'm reading this paper by Alfredo Iorio and I have a doubt concerning the anticommutation relations he uses for the Dirac field.
Around eq. (2.25), he wants to find the unitary operator $U$ that ...
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Why do we only consider commutators and anticommutators in QFT?
While studying canonical quantization in QFT, I observed that we quantize fields either by a commutation or an anticommutation relation
\begin{equation}
[\phi(x), \phi(y)]_\pm := \phi(x) \phi(y) \pm \...
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