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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Why is the quantum harmonic oscillator model used when an electromagnetic field is quantised?

I'm reading textbooks for quantum optics, and then see that every textbook introduces the quantisation of light, for which each book employs the quantum harmonic oscillator model. Why is this ...
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A condition on commutator implies quantization of field

The canonical quantization procedure requires pairs of conjugate dynamical variables to be identified, which, after quantization, become operators whose commutator is $i\hbar$. How does the second ...
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Quantization prescription for an interacting field theory

To my understanding, unlike free fields, interacting fields cannot be expanded in terms of Fourier modes, with the Fourier coefficients representing creation and annihilation operators. Then is it ...
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Quantized fields on Schwarzschild, QNM and bound states

In the process of quantization of a scalar field (in massive as in massless cases) propagating on a Schwarzschild background, we are first of all required to solve the equations of motion. Typically, ...
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Hedin's equations and the ground state energy

Hedin's equations are an iterative scheme to calculate the Green's function $G$, the self-energy $\Sigma$, the vertex $\Gamma$, the polarizability $\chi$, and the screened interaction $W$. However, ...
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Computing the density operator commutation relations (Atland & Simons)

I'm trying to work through Altland and Simons' example of interacting fermions in one dimension. It's in chapter 2, page 70 (you can find it here). They define fermionic operators $$a_{sk}^\dagger$$...
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Commutation Relations in Second Quantization

I understand that if I have the field operators $\psi(r)$ and $\psi^\dagger(r)$, then I have the canonical commutation relation (in the boson case) $$[ \psi(r) , \psi^\dagger(r')]=\delta(r-r').$$ My ...
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Derive Fermion Particle Density Operator in q-space

I am reading Bernevig's Topological Insulators and Topological Superconductors. In section 3.1.1, it gives an expression for the Fourier transformation of electron density operator, which I cannot ...
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What do the wave functions associated to the Fock states of each mode of a bound state system mean?

$\renewcommand{\ket}[1]{\left \lvert #1 \right \rangle}$ Consider a string of length $L$ under tension and clamped on each end. This system is described by the wave equation and has a set of modes. ...
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The Origins of the Second Quantization

I've been studying quantum theory for a while now and have a number of closely related questions that are not giving me any peace. I am not sure if such a long format is appropriate here, but I'd like ...
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why is the chemical potential included in the hamiltonian for a systeme coupeled to a particle reservoir

I am beginning with second quantification language so i saw that if we are in grand canonical ensemble then: $$H=H_0 - \mu N$$ naturally i thought that this $\mu$ would be included in the ...
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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 ...
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Canonical second quantization vs canonical quantization with multisymplectic form in AQFT

First of all, I'm a mathematician that knows less than the basics of QFT, so forgive me if this question is trivial. Please, keep in my mind that my background in physics is very poor. 1) The usual ...
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Second quantization and Hamiltonian diagonalization

So I want to diagonalize my Hamiltonian (it is bosonic hamiltonian) which is: $H=(E+\Delta)a^{\dagger}a + 1/2\Delta(a^{\dagger}a^{\dagger} + aa)$ My class didn't cover this material so I don't ...
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Problem using spin-restricted form of the second-quantized nonrelativistic Hamiltonian

I have a problem that confuses me a lot. The two-electron part of the electronic nonrelativistic Hamiltonian can be written \frac{1}{2}\sum_{pqrs} (pq|rs) [a^\dagger_{p\alpha}a^\...
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