Talk:Jordan–Wigner transformation

A few points,

1 It's probably worth explaining how this provides the correct commutation relations

2. There should be a section on the significance of this transform to quantum computing and the importance should reflect that. Lessconfusedthanbefore (talk) 15:32, 29 January 2021 (UTC)[reply]

Quick Reference

This review gives the following form for the JW transformation:

$a_{j}^{\dagger }\mapsto (\prod _{m<p}\sigma _{m}^{z})\sigma _{p}^{+}$

$a_{p}\mapsto (\prod _{m<p}\sigma _{m}^{z})\sigma _{p}^{-}$

$\sigma ^{\pm }\equiv (\sigma ^{x}\mp i\sigma ^{y})/2$

I think it could be useful to introduce it as a quick reference to the transformation in the article?

Miguelmurca (talk) 20:13, 1 August 2020 (UTC)[reply]

Spin-specific?

This article makes it sound like this transformation only applies to boolean / "spin" operators, like those from the Ising model; but doesn't exactly the same analysis apply to, say, 1D QHOs at each site, or more generally, any system of indistinguishable "particles" with a well-defined parity at each site, as long as it picks up a sign change under odd permutations of the site labels?

In particular, the last sentence of the lead seems like it's possibly overstated (and possible OR):

> This transformation actually shows that the distinction between spin-1/2 particles and fermions is nonexistent. 2600:1700:E4C0:40C0:45F1:AE1B:A4A4:A533 (talk) 19:17, 3 May 2025 (UTC)[reply]