- #1
paweld
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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%2F31%2F1946&_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%2F31%2F1946&_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.
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