Questions tagged [second-quantization]

Second quantization or canonical quantization in quantum field theory and many-body systems is the collective organizing and accounting of an infinity of quantum excitations and their interactions through quantum field operators.

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2answers
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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: \begin{...
8
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1answer
409 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] = \...
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3answers
403 views

EM field quantization

I'm trying to quantize the electromagnetic field by solving the vector potential wave equation, that is: $$\nabla^{2} \mathbf{A} = \dfrac{1}{c^{2}} \dfrac{\partial ^{2} \mathbf{A}}{\partial t^{2}}, $$...
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1answer
602 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 \...
4
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1answer
949 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. ...
10
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2answers
335 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)?
16
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3answers
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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
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2answers
1k 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 ...
6
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1answer
1k 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 ...
10
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2answers
1k 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 ...
28
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2answers
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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 ...
47
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9answers
6k 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 $x^\...