Questions tagged [anticommutator]
The anticommutator tag has no usage guidance.
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What is the connection between Poisson brackets and commutators?
The Poisson bracket is defined as:
$$\{f,g\} ~:=~ \sum_{i=1}^{N} \left[
\frac{\partial f}{\partial q_{i}} \frac{\partial g}{\partial p_{i}} -
\frac{\partial f}{\partial p_{i}} \frac{\partial g}{\...
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What is the Physical Meaning of Commutation of Two Operators?
I understand the mathematics of commutation relations and anti-commutation relations, but what does it physically mean for an observable (self-adjoint operator) to commute with another observable (...
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What is the physical meaning of anti-commutator in quantum mechanics?
I gained a lot of physical intuition about commutators by reading this topic.
What is the physical meaning of commutators in quantum mechanics?
I have similar questions about the anti-commutators. ...
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What is the meaning of the anti-commutator term in the uncertainty principle?
What is the meaning, mathematical or physical, of the anti-commutator term?
$$\langle ( \Delta A )^{2} \rangle \langle ( \Delta B )^{2} \rangle \geq \dfrac{1}{4} \vert \langle [ A,B ] \rangle \vert^{2}...
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Making sense of the canonical anti-commutation relations for Dirac spinors
When doing scalar QFT one typically imposes the famous 'canonical commutation relations' on the field and canonical momentum: $$[\phi(\vec x),\pi(\vec y)]=i\delta^3 (\vec x-\vec y)$$ at equal times ($...
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Fermions, different species and (anti-)commutation rules
My question is straightforward:
Do fermionic operators associated to different species commute or anticommute? Even if these operators have different quantum numbers? How can one prove this fact in a ...
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Why is the uncertainty principle not $\sigma_A^2 \sigma_B^2\geq(\langle A B\rangle +\langle B A\rangle -2 \langle A\rangle\langle B\rangle)^2/4$?
In Griffiths' QM, he uses two inequalities (here numbered as $(1)$ and $(2)$) to prove the following general uncertainty principle:
$$\sigma_A^2 \sigma_B^2\geq\left(\frac{1}{2i}\langle [\hat A ,\hat B]...
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The anticommutator of $SU(N)$ generators
For the Hermitian and traceless generators $T^A$ of the fundamental representation of the $SU(N)$ algebra the anticommutator can be written as
$$
\{T^A,T^{B}\} = \frac{1}{d}\delta^{AB}\cdot1\!\!1_{d} +...
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Causality for the Dirac Field
In Peskin & Schroeder page 54, they are trying to show how far they can take the idea of a commutator for the Dirac field instead of anti-commutator. To this end they are examining causality, ...
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Why are anticommutators needed in quantization of Dirac fields?
Why is the anticommutator actually needed in the canonical quantization of free Dirac field?
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Angular and linear momentum operators' commutation
Do linear and angular momentum operators commute? If I use the canonical commutation relations I get that they commute. Say, for $x$-component,
$[p_x, L_x] = p_x y p_z - y p_z p_x - p_x z p_y + z p_y ...
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Why do we use the anticommutation relation for particle-hole and chiral symmetries?
In physics we say that a quantity is conserved, if its operator commutes with Hamiltonian.
For example, in condensed matter systems, when the momentum $k$ commutes with the Hamiltonian $H$ as $[H,k]=...
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What goes wrong when one tries to quantize a scalar field with Fermi statistics?
At the end of section 9 on page 49 of Dirac's 1966 "Lectures on Quantum Field Theory" he says that if we quantize a real scalar field according to Fermi statistics [i.e., if we impose Canonical ...
user7154
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A few simple questions about Grassmann numbers: commutation relations and derivatives
I'm trying to learn about Grassmann numbers from the book "Condensed Matter Field Theory" by Altland and Simons, but I am currently encountering some difficulties. I have several smaller questions ...
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Proof of the Anti-Commutation Relation for Gamma Matrices from Dirac Equation
My textbook on QFT says that the Dirac equation can be used to show the following relation:
$$\{\gamma^{\mu},\gamma^{\nu}\}=2g^{\mu\nu}$$
I have searched around and unable to find how to prove this ...
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