Questions tagged [anticommutator]
The anticommutator tag has no usage guidance.
36
questions with no upvoted or accepted answers
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Explicit quantization of free fermionic field
The canonical quantization of a scalar field $\phi(x)$ can explicitly be realized in the space of functionals in fields $\phi(\vec x)$ (here $\vec x$ is spacial variable) by operators
\begin{eqnarray}
...
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Is $\overline{\psi_{L}^{c}}\psi_{R}^{c}=\overline{\psi_{R}}\psi_{L}$ true for two different spin 1/2 fermions?
In the context of seesaw mechanism or Dirac and Majorana mass terms, one often see the following identity
$$
\overline{\psi_{L}^{c}}\psi_{R}^{c}=\overline{\psi_{R}}\psi_{L}.
$$
Here, I am using 4 ...
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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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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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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
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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 ...
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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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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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How are Grassmann fields "forced upon us" by representation theory of $SO(d-1,1)$?
I would like to know if anticommuting fields (which physicists use as fermions) emerge naturally from the spin representation theory of $SO(d-1,1)$. Is the fact that spinor fields anticommute a ...
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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,
$$[\alpha_k^{\dagger}\alpha_k, \alpha_{k'}^{\dagger}(\nabla_{k'}\...
- 1,007
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Commutation of kinetic energy operator with Hamiltonian
I am basically trying to calculate current energy operator $\hat{\mathbf{J}}_E(\mathbf{r})$ by using Heisenberg equation of motion as
$$
-\nabla\cdot \hat{\mathbf{J}}_E(\mathbf{r})=\frac{i}{\hbar}[H,\...
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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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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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Do fermionic creation/annihilation anticommutation relations fix the creation and annihilation operators?
If you define operators $a, a^\dagger$ which satisfy (e.g.) the relations $\{a,a\}=\{a^\dagger,a^\dagger\}=0$ and $\{a,a^\dagger\}=1$.
Will this uniquely define the operators such that $a |0\rangle \...
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Anticommutation relation for the Weyl spinors in Minkowski space+time
For $D$-dimensional Minkowski space+time, I suppose that the Dirac spinor has the following anticommutation relation:
$$
\{ \psi(x_1), \psi(x_2)\}=\{ \psi^\dagger(x_1), \psi^\dagger(x_2)\}=0
$$
$$
\{ \...
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