Talk:Bogoliubov transformation

This article has been labeled as lacking sources. Aren't references the article cites sufficient sources? --bonzi (talk) 21:15, 6 January 2008 (UTC)

Regarding the first section, some comments: A Bogoliubov trafo is NOT unitary! It has to be a symplectic transformation. In particular, there exist counter examples where the unitarity and symplecticity contradict each other. In the case where v=0, the transform is of course unitary. I request to change this sentence. Mashout1718 (talk) 17:40, 10 July 2009 (UTC)

If you have a reference for this point please go ahead and change it, citing the reference! Grj23 (talk) 03:37, 2 September 2009 (UTC)

The nature of the transformation depends on the objects it is acting on. This leads to the above mis-understanding. The transformation is symplectic when applied to the classical position and momentum coordinates (the name canonical transformation from classical mechanics is equivalent). The transformation could be called canonical when applied to the quantized position and momentum operators, or to the creation and annihilation operators, as exemplified in this wiki -- the name conveys that the transformed operators still obey the same canonical commutation relations. And finally, if the transformation is made to act on the states that these operators act on, it is represented, indeed, by a unitary operator. Since symplectic transformations do not form a compact group (they can be parametrized by parameters taken from the entire set of real numbers), the state space they act on as unitaries must be infinite-dimensional. This is a standard theorem of group theory. DieHenkels (talk) 12:44, 20 March 2015 (UTC)

A second mistake: The second relation of the canonical (anti-)commutation relations, namely [a,a]=0, is not mentioned. For the single boson this is of no importance (since uv-uv=0). However, it is relevant for fermions since here one would get the constraint uv+uv=0 for a single fermionic mode which can only be satisfied by either u=0 or v=0. Consequence: One needs to consider at least two modes (e.g. spin up and down). Hence I would suggest to delete the paragraph about the single fermionic mode altogether and to extend the multi-mode section instead (referring to Bogoliubov-de Gennes Hamiltonians, see recent literature about topological insulators).Seraphimir (talk) 15:05, 17 May 2011 (UTC)

Clarity

I feel this article fails to make clear why or how Bogoliubov transformations are used. Is it possible that a simple example could be given? Grj23 (talk) 03:37, 2 September 2009 (UTC)

Bogoliubov superfluidity

I can't find a reference for Bogoliubov paper to superfluidity 1947, it seems it has the same name as Landau's (1949) and it precedes it. If some work about it was made it must be after BCS. MaoGo (talk) 19:34, 5 April 2016 (UTC)

It was published (in English) in a short-lived journal called Journal of Physics of the USSR, Vol 11 p. 23 (1947). There is a scan of it at ufn.ru/pdf/jphysussr/1947/11_1/3jphysussr19471101.pdf — Preceding unsigned comment added by 74.136.34.4 (talk) 02:08, 8 April 2017 (UTC)

Needs introduction for non-experts

The article needs a simplified explanation to introduce it to non-experts. It needs to be explained (at an overview level) just what the transformation is. Geoffrey.landis (talk) 17:34, 28 August 2019 (UTC)

Added "chiral fermion" to section Fermionic mode

Unfortunately, "chiral fermion" redirects to spinor, where there is no mention of chirality anywhere. The more nearly correct redirect would be to chirality. Anybody know how to change such redirects?MidwestGeek (talk) 21:26, 29 January 2020 (UTC)