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0answers
95 views

Second quantization with qubits

Is "second quantization" means system wich can contain variable, unknown, superposed and otherwise uncertain number of qubits? Can "second quantized" system contain 0.5% of 1 qubit and 95% of 2 ...
4
votes
2answers
320 views

Second Quantization - Texts

I am trying to familiarize myself with the ideas of Second Quantization. However, the literature that I can find online seems only to outline the tools of this formalism of quantum mechanics. There ...
2
votes
1answer
173 views

Reason behind canonical quantization in QFT?

Reason behind canonical quantization in QFT? In the scalar field theory we simply promote the scalar field, $\phi(x)$ to a set of operators: $\hat{\phi}(x)$. What is the reason behind this?
3
votes
2answers
300 views

Composition of squeeze operators?

I'm wondering if it exists a composition law for the squeezing operation ? I guess so for geometric reason, since they are (generalized, and the phase is annoying of course) hyperbolic rotations of ...
2
votes
1answer
116 views

One body harmonic oscillator states expressed in terms of creation operators

I am reading trough chapter one of Moshinsky's "The harmonic Oscillator in Modern Physics". However i am having some trouble with the mathematics in section 8 of chapter 1. I will sketch a summary of ...
1
vote
0answers
124 views

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 ...
8
votes
1answer
386 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" ...
3
votes
2answers
380 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
175 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?
5
votes
1answer
589 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
241 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
205 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: ...
5
votes
1answer
227 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
268 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
votes
1answer
262 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
370 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. ...
8
votes
2answers
222 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)?
13
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3answers
1k 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
580 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 ...
8
votes
1answer
626 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 ...
9
votes
2answers
811 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 ...
15
votes
1answer
5k 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 ...
33
votes
9answers
3k 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 ...