The second-quantization tag has no wiki summary.
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Time ordering and Fermions
Having time ordering operator for fermions, should it reverse sign if it swaps operators with opposite spin variable? In other words should
$T[c_{t_1,\uparrow}c_{t_2,\downarrow}^\dagger]$
return ...
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0answers
106 views
Some questions about anyons?
(1) As we know, we have theories of second quantization for both bosons and fermions. That is, let $W_N$ be the $N$ identical particle Hilbert space of bosons or fermions, then the "many particle" ...
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Spin operators in second quantization [closed]
I've got hamiltonian in form:
$H = \sum\limits_{lm}a_{lm}^{+}a_{lm}H_{lm} + \sum\limits_{ijml}J_{ijml}a_{j}^{+}a_{m}^{+}a_{l}a_{i}$.
How can I substitute the spin operators in this system. I'd like ...
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1answer
85 views
Density operator in second quantization
I would want to understand why the density operator in second quantization takes the form:
$$\rho_\sigma(\mathbf{r})=\Psi_\sigma^\dagger(\mathbf{r})\Psi_\sigma(\mathbf{r})?$$
Is this a definition or ...
1
vote
1answer
53 views
Classical second quantization paper by Jordan and Wigner - ref. request [closed]
I am looking for the following paper in electronic format (I can get it in hard copy from my university library).
P. Jordan and E. Wigner, Z. Phys. 47, 631 (1928)
Does anyone know how to find it?
4
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1answer
186 views
How to evaluate spin operators in second quantization for spin symmetry-broken Slater determinants?
Suppose we have the following Slater determinant:
\begin{equation}
| \Psi \rangle = \prod \limits_{i,i'} a^+_{i\alpha} a^+_{i'\beta} | \rangle
\end{equation}
where $a^+_{i\alpha}$ creates an electron ...
4
votes
1answer
100 views
Why is the Wick contraction in HFB or BCS equal to a single-particle density?
I'm trying to understand how in Hartree-Fock-Bogoliubov
(HFB) or BCS theory we can write a product of creation/annihilation operators as single-particle densities under the guise of "Wick's theorem".
...
7
votes
2answers
125 views
Scalar product between Fock states
Suppose to have a chain (of size $L$) with bosons, and $\hat{a}_i^\dagger$,$\hat{a}_i$ are the associated creation and annihilation operators at site $i$. A Fock state can be written as:
...
4
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1answer
135 views
Is it possible to make statements about bosonic/fermionic systems by taking the limit $\theta\to \pi$ or $\theta\to 0$, of an anyonic system?
One might naïvely write the (anti-)commutation relations for bosonic/fermionic ladder operators as limits
$$
\delta_{k,\ell} = \bigl[ \hat{b}_{k}, \hat{b}_{\ell}^\dagger \bigr]
= ...
1
vote
3answers
200 views
EM field quantization
I'm trying to quantize the electromagnetic field by solving the vector potential wave equation, that is:
$$\nabla^{2} \mathbf{A} = \dfrac{1}{c^{2}} \dfrac{\partial ^{2} \mathbf{A}}{\partial t^{2}}, ...
2
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1answer
136 views
A missing factor of 2 in the standard Hartree-Fock mean field?
Let's start from a very simple argument: If $A$ and $B$ are some operators, then I can write their product as
$$AB = (A-\langle A\rangle)(B - \langle B \rangle) + \langle A \rangle B + A \langle B ...
2
votes
1answer
167 views
Symbolic tool for doing 2nd quantization operator calculations
I think everyone who has attended a lecture introducing second quantization appreciates what a pain it can be to compute expressions involving commutators or anticommutators with lots of operators.
...
7
votes
2answers
181 views
Finding the spectrum of a polynomial of the creation and annihilation operators
Is there a general algorithm to find the spectrum of $S S^\dagger$, where $S$ is a homogenous polynomial (of degree $n$) of the annihilation operators (of $d$ variables)?
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3answers
824 views
What does the ordering of creation/annihilation operators mean?
When a system is expressed in terms of creation and annihilation operators for bosonic/fermionic modes, what exactly is the physical meaning of the order in which the operators act?
For example, for ...
2
votes
2answers
410 views
Scalar product of coherent states
We suppose for semplicity to have a 1D oscillator, but this is a question abaout the general CCR algebra in oscillators, second quantization, quantum field theory etc.
We know coherent states are a ...
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vote
0answers
256 views
Quantization of Gravitational Field: Quantization conditions
I'm begining to study Quantization of field with the second quantization formalism. I've studied phononic field, electromagnetic field in the vacuum and a generic relativistical scalar field.
I ...
7
votes
2answers
556 views
What does second quantization mean in the context of string theory?
String field theory (in which string theory undergoes "second quantization") seems to reside in the backwaters of discussions of string theory. What does second quantization mean in the context of a ...
7
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1answer
3k views
Kubo Formula for Quantum Hall Effect
I'm trying to understand the Kubo Formula for the electrical conductivity in the context of the Quantum Hall Effect.
My problem is that several papers, for instance the famous TKNN (1982) paper, or ...
21
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9answers
2k views
Is a “third quantization” possible?
Classical mechanics: $t\mapsto \vec x(t)$, the world is described by particle trajectories $\vec x(t)$ or $x^\mu(\lambda)$, i.e. the Hilbert vector is the particle coordinate function $\vec x$ (or ...
