# Questions tagged [anticommutator]

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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 $P$...
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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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### Relationship between anti-commutators and correlation

Ballentine (in his solution at the back of the book to his Problem 8.10) writes that $$[Tr(\rho \{A,B\}/2)]^2$$ is related to the correlation between the observables represented by $A,B$, but gives no ...
1 vote
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### Anticommutator Relation of Quantized Fermionic Field and Fermi–Dirac statistics: How are these related?

I'm reading the Wikipedia article about Fermionic field and have some troubles to understand the meaning following phrase: We impose an anticommutator relation (as opposed to a commutation relation ...
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### Anti-commutation relation for gamma matrices; when/why did the definition change?

The anti-commutation relation defining gamma matrices is presently given by $$\gamma^\mu \gamma^\nu + \gamma^\nu \gamma^\mu = 2g^{\mu\nu}$$ where appears the matric tensor (see for instance the ...
1 vote
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### From Fermions to CAR

I do not understand why Fermions statistic is equivalent to the CAR. In other words, suppose we have $\{a_i\}_i$ set of Fermionic operators acting on an Hilbert space, they satisfy the Canonical ...
### How should I imagine a spinor commutator, or consecutive occurences of $\bar{\Psi}$ and $\Psi$ in general?
I'm having a hard time making sense of an expression like $$\left[\Psi(x), \bar{\Psi}(y)\right].$$ Up until now I imagined a spinor operator to be something like a column vector of operators, ...