# 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.

54 questions
Filter by
Sorted by
Tagged with
1answer
2k views

### 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 ...
3answers
4k views

### 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 ...
3answers
3k 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 ...
3answers
2k views

### 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 ...
3answers
3k views

### 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 ...
3answers
754 views

### What do the wave functions associated to the Fock states of each mode of a bound state system mean?

$\renewcommand{\ket}{\left \lvert #1 \right \rangle}$ 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. ...
2answers
9k 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 ...
4answers
5k views

2answers
196 views

### What is the precise formal correspondance between an oscillator and a quantum field?

A common route of introduction to quantum field theory is to note a similarity between the mathematical structure of a quantum harmonic oscillator and of a quantum field "at a point". The quantised ...
0answers
120 views

### Fetter & Walecka's derivation of second quantised canonical Schrodinger equation for fermions

On page 18, before the occupation number variables for states i and j are changed $n_i \rightarrow n'_i = n_i - 1$ and $n_j \rightarrow n'_j = n_j + 1$ respectively, could we not have rewritten eq. 1....
9answers
6k views

1answer
101 views

### Dispersion relation in tight binding model with even indices only

Given a tight binding model with Hamiltonian $H= \sum_{i(even)}t[c_{i+1}^\dagger c_i+h.c]$ containing even indices only, how can we find out the dispersion relation? Attempt: My guess is that the ...
1answer
2k views

### First quantization vs second quantization

What is the difference between first quantization and second quantization and where does the name second quantization come from?
1answer
791 views

### Second Quantization in Condensed Matter and Quantum Field Theory

There appears to be an apparent dichotomy between the interpretation of second quantized operators in condensed matter and quantum field theory proper. For example, if we look at Peskin and Schroeder, ...
0answers
178 views

### Fock Subspaces and Weight Vectors

This is my first time taking a physics course (I'm a mathematics major), so I'm encountering a lot of new things, which I'm kind of expected to know. In particular, how to work with Bosons. I've got ...
1answer
220 views

1answer
140 views

### Expansion coefficients in the solution of the Dirac equation for a free particle

So my question is why do we need to write the coefficients $b$ (that after the second quantization are going to be promoted as the antiparticle creation operators) as complex conjugate? I mean, why ...