All Questions
Tagged with anticommutator quantum-field-theory
73
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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
$$
\{\psi(x), \...
- 41
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1
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$C$-number ignored in charge conjugation
In Weinberg’s QFT V1, under equation 5.5.58, he says that an anticommutator ($c$-number) can be ignored when we exchange spinors, $\psi$ and $\bar{\psi}$. I cannot fully appreciate why we can ignore ...
- 529
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Does the anticommutator of two spinors affect the transpose of their product?
My lecture notes claim that for an anticommutation relation
$$[ \psi_{\mu}(\bf{x},t),{\psi_{{\nu}}^{*}}(\bf{y},t)] = \delta_{\mu \nu} \delta^3(\bf{x}-\bf{y})$$
between two spinors, the transpose of ...
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Product of spinors in Dirac field anticommutators
I am reading a "A modern introduction to quantum field theory" by Maggiore and on page 88 it shows the anticommutators of the Dirac field:
$$
\{\psi_a(\vec{x},t),\psi_{b}^{\dagger}(\vec{y},t)...
- 613
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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}
\...
- 1,669
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111
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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 $$\mathcal L = i\bar\psi\gamma^\mu\partial_\mu\psi\...
- 21
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Why is commutation bracket used instead of anti-commutation bracket on page 61 of Peskin QFT?
Peskin&Schroeder was performing a trick where they used
$$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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49
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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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145
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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 ...
- 2,284
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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 ...
- 1,395
2
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0
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68
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Can Exceptional Jordan Quantum mechanics model field theory?
Exceptional Jordan Quantum mechanics is an interesting case in which observables are modelled with $3\times3$ Hermitian octonion matrices $\mathbb{J}_3(\mathbb{O})$. There is the Jordan product $A\...
user84158
2
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123
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About the Hilbert space that carries the representation of $\{\psi (x), \bar{\psi (y) }\}=i\delta (x-y) $?
What is this Hilbert space? Is it the complex Hilbert space of wavefunctionals spanned by using the spinor-field configurations as the basis vectors?
I know that the wavefunctional space carries a ...
- 6,355
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116
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Dirac spinor field anti-commutation
I am thinking the anti-commutation property of Dirac field! First, note that the equal time anti-commutation relation (from P&S's QFT):
$$\{ \psi_a(\mathbf{x}),\psi_b^{\dagger}(\mathbf{y}) \}=\...
- 1,421
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Where do arbitrary phases of wavefunctions go under second-quantization?
As far as I understand, a second-quantized operator in QFT or condensed matter represents a many-body wavefunction (symmetrized for bosons or antisymmetrized for fermions). But every wavefunction is ...
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Electron fields does not anticommute at space-like points
In the end of page 804 and beginning of page 805 of Streater's paper
Outline of axiomatic relativistic quantum field theory
which can be find here https://iopscience.iop.org/article/10.1088/0034-4885/...
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