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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.

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. The quantum many-body states are represented in Fock space, consisting of an infinity of single-particle states filled up with a certain number of identical particles.

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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 $x^\mu$), which is then projected into the space…
Tobias Kienzler
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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 an elaboration by Kohmoto (1984), write the…
Greg Graviton
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Bogoliubov transformation is not unitary transformation, correct?

To diagonalize quadratic term in the antiferromagnet Heisenberg model, we may introduce the Bogoliubov transformation:$a_k=u_k\alpha_k+v_k\beta_k^\dagger$, $b_k^\dagger=v_k\alpha_k+u_k\beta_k^\dagger$. This transformation can diagonalize the…
ZJX
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What is the physical interpretation of second quantization?

One way that second quantization is motivated in an introductory text (QFT, Schwartz) is: The general solution to a Lorentz-invariant field equation is an integral over plane waves (Fourier decomposition of the field). Each term of the plane wave…
yjc
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How exactly is "normal-ordering an operator" defined?

(In this question, I'm only talking about the second-quantization version of normal ordering, not the CFT version.) Most sources (e.g. Wikipedia) very quickly define normal-ordering as "reordering all the ladder operators so that all of the creation…
tparker
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Difference between field and wavefunction

Can someone give me a clear explanation of what is the difference between a classical field, a wave function of a particle and a quantum field? I haven't find a clear explanation. For example for Klein-Gordon equation, the solution $\phi(x)$ is a…
Silviu
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Can a theory gain symmetries through quantum corrections?

It is well known that not all symmetries are preserved when quantising a theory, as evinced by renormalising composite operators or by other means, which show that quantum corrections may alter a conservation law, such as with the chiral anomaly, or…
user2062542
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In what sense is a quantum field an infinite set of harmonic oscillators?

In what sense is a quantum field an infinite set of harmonic oscillators, one at each space-time point? When is it useful to think of a quantum field this way? The book I'm reading now, QFT by Klauber, claims its not true, which is it? I would like…
user41404
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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 to seize this opportunity and share my questions…
mavzolej
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Schrödinger equation from Klein-Gordon equation?

One can view QM as a 0+1 dimensional QFT, fields are only depending on time and so are only called operators, and I know a way to derive Schrödinger's equation from Klein-Gordon's one. Assuming a field $\Phi$ with a low energy $ E \approx m $ with…
toot
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Are photons actually particles at all?

I just read this answer to "What exactly is a Photon?" which has me a bit confused. It seems to be arguing that "photon" is just a catch-all term for any sort of interaction with the EM field and the implication is that it's not even a particularly…
Mikayla Eckel Cifrese
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Schrödinger wavefunctional quantum-field eigenstates

The reason that I have this problem is that I'm trying to solve problem 14.4 of Schwartz's QFT book, which've confused me for a long time. The problem is to construct the eigenstates of a quantum field $\hat{\phi}(\vec{x})$, such that…
Nahc
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Quantizing a complex Klein-Gordon Field: Why are there two types of excitations?

In most references I've seen (see, for example, Peskin and Schroeder problem 2.2, or section 2.5 here), one constructs the field operator $\hat{\phi}$ for the complex Klein-Gordon field as follows: First, you take the Lagrangian density for the…
Jahan Claes
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Can we "trivialize" the equivalence between canonical quantization of fields and second quantization of particles?

As Weinberg exposited in his QFT Vol1, there are two equivalent ways of arriving at the same quantum field theories: (1). Start with single-particle representations of Poincare group, and then make a multiparticle theory out of it, while preserving…
Jia Yiyang
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First quantization vs second quantization

What is the difference between first quantization and second quantization and where does the name second quantization come from?
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