All Questions
12
questions
1
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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
0
votes
0
answers
67
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Rewriting two-body operator in second-quantized form
I would like to understand the following identity for fermion field operators:
$$\psi^\dagger(x) \psi^\dagger(y) \psi(y) \psi(x) = \psi^\dagger(x) \psi(x) \psi^\dagger(y) \psi(y) - \delta(x - y) \psi^\...
2
votes
2
answers
1k
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Using Grassmann variables on fermionic theories
I think the best way to put my question is the following: what (fermionic) theories make use of Grassmann variables?
Let me clarify my question a little further. I remember some discussions in quantum ...
- 585
3
votes
1
answer
722
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Minus Sign in Fermionic Creation and Annihilation Operators
I have the same question as the person here:
Action of Fermionic Creation and Annihilation Operators
The question actually wasn't anwered, because using anticommutation relations between creation $c_\...
- 182
1
vote
1
answer
201
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Second quantisation for fermions
I am trying to build a model for reactions on a lattice in the Doi-Peliti formalism. Suppose there exists a lattice of $N$ sites indexed by $i$. Each site can be either occupied or unoccupied. ...
- 141
2
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1
answer
1k
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Bogoliubov transformation for fermionic Hamiltonian
I have the Hamiltonian
$H=\sum\limits_k [Ab^{\dagger}_{k}b_{k} + B(b^{\dagger}_kb^{\dagger}_{-k}+b_{k}b_{-k})]$,
where $b^{\dagger}_k$ and $b_k$ are fermionic creation and annihilation operators.
...
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1
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1
answer
288
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Can a general many-body Hamiltonian with quadratic and biquadratic terms be diagonalized?
Can an arbitrary many-body hamiltonian in second quantization form with quadratic and biquadratic terms
$$H=\sum_{v_1,v_2} \alpha_{v_1 v_2}\ c_{v_1}^{\dagger}c_{v_2}+ \sum_{v_1,v_2,v_3,v_4}\beta_{v_1 ...
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1
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2
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2k
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Deriving anti-commutation relation between creation/annihilation operators for Dirac fermions
Starting from Dirac fields:
$$\Psi(x) = \dfrac{1}{(2\pi)^{3/2}} \int \dfrac{d^3k}{\sqrt{2\omega_k}}\sum_r\left[ c_r(k)u_r(k)e^{-ikx}+d^\dagger_r(k)v_r(k)e^{-ikx} \right]_{k_0=\omega_k}$$
$$\Psi^\...
- 23
2
votes
1
answer
194
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Spinor quantization: contradiction between covariant anticommutator and canonical rules?
Starting from the free lagrangian
$$\mathscr L = \bar\Psi(i\displaystyle{\not}\partial - m)\Psi$$
I compute the canonical momenta
$$\Pi =\frac{\partial \mathscr L}{\partial\dot{\Psi}}=i\Psi^\dagger ...
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1
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0
answers
83
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Some subtleties in quantizing a fermi field
Consider the quantization conditions for a complex Fermi field $\Psi=\Phi_1+i\Phi_2$:
$$\{\Psi(x),\Psi(y)\}=\{\Psi^\dagger(x)\Psi^\dagger(y)\}=0,~~~~ \{\Psi^\dagger(x),\Psi(y)\}=\delta(x-y)$$
Compare ...
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1
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0
answers
146
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Definition of partity in quantized Dirac Theory.
I'm studying from the book "An Introduction to Quantum Field Theory" from Michael E. Peskin and Daniel V. Schroeder, and I read the following:
"The operator P should reverse momentum of a particle ...
1
vote
1
answer
295
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Matrix elements of a one-fermion operator (first and second quantizations)
I'm currently struggling with the expression of operators in second quantization. I did an exercise in which I had to consider a fermion in a central potential $V(\vec{r})$ and show that the matrix ...
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