Questions tagged [anticommutator]
The anticommutator tag has no usage guidance.
169
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How do fermionic operators transform?
In quantum mechanics, if we have an operator $\Omega$, then under the transformation $T$, with infinitesimal generator $G$ (i.e. $T(\epsilon)=1-i\epsilon G + \ldots$), then operator transforms as
$$\...
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1
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Creation and annihilation operators for fermions from anticommutator
In a question, I was given that $a^{\dagger}a + a a^{\dagger} =1$ and asked to show what $a|n\rangle$ and $a^{\dagger}|n\rangle$ would be, given that $H|n\rangle=(a^{\dagger}a + 1/2)$.
I am getting ...
- 182
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(Anti)commutators at different times
Why does the commutator of two operators evaluated at different times vanish? Take for instance a fermonic field $\psi_\sigma (\vec{x},t)$, which satisfies the well known anti-commutation relations ...
- 314
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Anticommutator of gauge covariant derivatives
I must convert some dimension-6 operators I've obtained to the SILH base (ref: this, "Review of the SILH basis", CERN presentation by R. Contino).
In this conversion I've got operators such ...
- 127
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(Anti)commutation relations for higher-dimensional anti-symmetrized Gamma matrices
Suppose $a,b,c...=0,....,D-1$ are Lorentz indices of $SO(1,D-1)$ tangent space and consider $D$-dimensional Clifford algebra defined by the usual anticommutation relation
$$\{\Gamma^a,\Gamma^b\}=2\eta^...
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How to solve differential equation involving commutator and anti-commutator?
In one of my exercise, I got following differential equation for density matrix $\rho$,
$$
\frac{d\rho}{dt}=-i[H_1,\rho]+\{H_2,\rho\}
$$
where $H_1$ and $H_2$ are the Hermitian Hamiltonian, and $[.,.]$...
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How do you experimentally realise the operator of the form $\hat{A}\hat{B}+\hat{B}\hat{A}$?
I was reading a paper in which the authors use the operator of the form $\hat{A}\hat{B}+\hat{B}\hat{A}$ and it is implied to be experimentally realisable.
(i.e either creating an apparatus to ...
- 115
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Is there a bosonic representation of Clifford algebra in (1,3) spacetime?
By a suitable combination of Dirac's $\gamma_\mu$ matrices one can define creation and destruction operators satisfying fermionic anticommutators. Is there a similar result for bosons in the context ...
1
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1
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Finding chiral-symmetric degenerate states numerically
I am dealing with a Chiral-symmetric Hamiltonian such that
$$
𝑆𝐻𝑆^{−1}=−𝐻.
$$
Two of its eigenstates have zero eigenvalue and fulfill $𝑆∣𝜓_{\alpha}⟩=𝑒^{𝑖𝜙_{\alpha}}∣𝜓_{\alpha}⟩$, while the ...
0
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Trick with "functional" derivative to evaluate commutators between diagonal hamiltonian and creation fermionic operator
I found a theorem that states that if $A$ and $B$ are 2 endomorphism that satisfies $[A,[A,B]]=[B,[A,B]]=0$ then $[A,F(B)]=[A,B]F'(B)=[A,B]\frac{\partial F(B)}{\partial B}$.
Now i'm trying to apply ...
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Is there an identity for anti-commutator $\{ A B, \, C D \}$ in terms of commutators $[\, , \,]$ only?
I'm looking for an identity that could express the anti-commutator
$$\tag{1}
\{ A B , \, C D \} \equiv A B C D + C D A B
$$
expressed as a combination of commutators only: $[A,\, C]$, $[A, \, D]$, etc....
- 7,592
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Anti-commutator for annihilation and creation operators: ordering of indices
I'm trying to prove that $\{\tilde a_i,\tilde a_j^{\dagger} \}=\delta_{ij}$, by defining
$\tilde a_i=\sum_j \bar U_{ji}a_j$. U is an unitary matrix and $a_i$ refers to an element of the operator $a$. ...
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$\mathcal{N} \ge 2$ Supersymmetry massive supermultiplets
In Bertolinis SUSY notes [https://people.sissa.it/~bertmat/susycourse.pdf] we have defined:
$$
\{Q^I_\alpha,\bar{Q}_\dot{\beta}^J\}=2m\delta_{\alpha\dot{\beta}}\delta^{IJ}\tag{3.24}
$$
$$
\{Q^I_\alpha,...
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Chiral Symmetry and Charge Algebra
I'm following Section 5.1 in Cheng and Li's Particle Physics book and I am having trouble reproducing some of the commutation relations.
The axial current is given by
$$
(J_A^a)^\mu = \bar{\psi}_\...
- 574
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1
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Importance of position of Bosonic and Fermionic operators in quantum mechanics
In quantum mechanics if (Fermionic or Bosonic) operators do not commute with each other, one cannot swap position of two operators easily. For example, let $(c^\dagger, c)$ are Fermionic operators, ...
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