- 255

- 0

I've found recently that there is very interesting theorem about quantization

procedure which states that the Dirac procedure of exchanging Poisson bracket

to commutator can't work for observables which are of order grater then 2 in momentum

or position (no matter which ordering we chose). This is Groenewold-van Hove theorem.

Unfortunately I cannot find the precise formulation of it. I don't know what assumption

are needed there. This theorem probably comes from the paper

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6X42-4FW6JXD-4&_user=3934946&_coverDate=10/31/1946&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1630632579&_rerunOrigin=scholar.google&_acct=C000054122&_version=1&_urlVersion=0&_userid=3934946&md5=03eadd9bb38467a28554de78206452a5&searchtype=a"

(but I don't have access to papers on ScienceDirect ...).

Could anyone give me a reference to diferent paper or state the

assumptions needed in this theorem.

procedure which states that the Dirac procedure of exchanging Poisson bracket

to commutator can't work for observables which are of order grater then 2 in momentum

or position (no matter which ordering we chose). This is Groenewold-van Hove theorem.

Unfortunately I cannot find the precise formulation of it. I don't know what assumption

are needed there. This theorem probably comes from the paper

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6X42-4FW6JXD-4&_user=3934946&_coverDate=10/31/1946&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1630632579&_rerunOrigin=scholar.google&_acct=C000054122&_version=1&_urlVersion=0&_userid=3934946&md5=03eadd9bb38467a28554de78206452a5&searchtype=a"

(but I don't have access to papers on ScienceDirect ...).

Could anyone give me a reference to diferent paper or state the

assumptions needed in this theorem.

Last edited by a moderator: