All Questions
Tagged with anticommutator fermions
74
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Canonical Variables in Dirac Spinor Field Theory
In S.Weinberg [QFT V1][1] section 7.1, in eq (7.1.15) and (7.1.16), he states that in order to be consistent with the previous-derived anti-commutator relation, we should take $\psi_{\text{n}}$ and $\...
- 529
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61
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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,
$$[\alpha_k^{\dagger}\alpha_k, \alpha_{k'}^{\dagger}(\nabla_{k'}\...
- 1,007
2
votes
1
answer
74
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Product of spinors in Dirac field anticommutators
I am reading a "A modern introduction to quantum field theory" by Maggiore and on page 88 it shows the anticommutators of the Dirac field:
$$
\{\psi_a(\vec{x},t),\psi_{b}^{\dagger}(\vec{y},t)...
- 613
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1
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100
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Confusion about whether a fermion field and its conjugate as an Grassmann number
I'm confused about what "a Grassmann-odd number" really means and how does it apply to fermions.
In some text, it says that "if $\varepsilon \eta+\eta \varepsilon =0 $, then $\...
- 368
3
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2
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456
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Geometry of anticommutation relations
I am asking this question as a mathematician trying to understand quantum theory, so please forgive my naivety.
Systems satisfying the canonical commutation relations are naturally modeled with ...
- 45
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2
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212
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Why does $[Q,P]=i\hbar$ work for fermion? Shouldn't fermion satisfy anticommuting relation?
For hydrogen, we use $[Q,P]=i\hbar$ for electron, which is a fermion. Does it have a deeper reason such as that we're really considering the proton + electron system, which might be of bosonic nature?
- 619
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1
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215
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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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88
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Help with commutator algebra with fermionic operators
I am struggling to understand how the following is true for the fermionic creation/annihilation operators $a^\dagger, a$: $$[a^\dagger a, a]=-a$$
If someone could walk me through the math derivation ...
- 101
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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
4
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1
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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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1
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125
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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 \...
- 1,588
1
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1
answer
66
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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
3
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1
answer
98
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Contour integral for commutator of fermionic fields
Suppose we have primary fields $A$ and $B$ which have the OPE,
$$A(z) B(w) = \frac{1}{z-w} = -B(z)A(w), \quad |z| > |w|,\tag{1}$$
so they have fermionic statistics. Now I was curious how this would ...
- 721
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1
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128
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Can Hadamard's formula be used for fermionic operators?
Can I use this special case of Hadamard's formula
$$e^\hat B \hat A e^{-\hat B}= A + [B,A]+\frac{1}{2!}[B, [B,A]] + \dots$$
for fermionic operators?
Suppose I have fermionic operators that obey ...
- 179
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Adding a surface term to Dirac action modifies the canonical anticommutation relations [duplicate]
I'm dealing with the following issue: when describing a fermionic field, one can use the typical Dirac Lagrangian $$\mathcal{L}=\bar\psi(i\gamma^\mu\partial_\mu-m)\psi,\tag{1}$$ or the more symmetric ...
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