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13
votes
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 ...
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 ...
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 ...
13
votes
5answers
526 views

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 ...
9
votes
2answers
814 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 ...
10
votes
3answers
297 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 ...
5
votes
1answer
228 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] = ...
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
0answers
152 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 ...
2
votes
4answers
319 views

Bogoliubov transformation with a slight twist

Given a Hamiltonian of the form $H=\sum_k \begin{pmatrix}a_k^\dagger & b_k^\dagger \end{pmatrix} \begin{pmatrix}\omega_0 & \Omega f_k \\ \Omega f_k^* & \omega_0\end{pmatrix} ...
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 ...