Comments on: Some notes on Weyl quantisation
https://terrytao.wordpress.com/2012/10/07/some-notes-on-weyl-quantisation/
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence TaoThu, 24 Aug 2017 06:16:53 +0000hourly1http://wordpress.com/By: Semiclassical Mechanics of the Wigner 6j-Symbol by Aquilanti et al | quantumtetrahedron
https://terrytao.wordpress.com/2012/10/07/some-notes-on-weyl-quantisation/#comment-359224
Sun, 01 Jun 2014 16:19:38 +0000http://terrytao.wordpress.com/?p=6213#comment-359224[…] Some notes on Weyl quantisation (terrytao.wordpress.com) […]
]]>By: Review of wigner nj-Symbols | quantumtetrahedron
https://terrytao.wordpress.com/2012/10/07/some-notes-on-weyl-quantisation/#comment-347735
Tue, 20 May 2014 19:58:56 +0000http://terrytao.wordpress.com/?p=6213#comment-347735[…] Some notes on Weyl quantisation (terrytao.wordpress.com) […]
]]>By: Lars Hormander « What’s new
https://terrytao.wordpress.com/2012/10/07/some-notes-on-weyl-quantisation/#comment-198030
Fri, 30 Nov 2012 19:53:10 +0000http://terrytao.wordpress.com/?p=6213#comment-198030[…] to multiplying a phase space distribution by the symbol of that operator, as discussed in this previous blog post. Note that such operators only change the amplitude of the phase space distribution, but not the […]
]]>By: Marcelo de Almeida
https://terrytao.wordpress.com/2012/10/07/some-notes-on-weyl-quantisation/#comment-189507
Mon, 05 Nov 2012 02:08:16 +0000http://terrytao.wordpress.com/?p=6213#comment-189507Reblogged this on Being simple.
]]>By: º«µÀÔª
https://terrytao.wordpress.com/2012/10/07/some-notes-on-weyl-quantisation/#comment-184184
Sat, 20 Oct 2012 11:35:53 +0000http://terrytao.wordpress.com/?p=6213#comment-184184I appreciate it very much that you send every new post of ‘what’s new’, however could you please send me the whole post rather than just a part of it.

Yours sincere,

Han Daoyuan

Sent from my iPad

]]>By: Sam Sachdev
https://terrytao.wordpress.com/2012/10/07/some-notes-on-weyl-quantisation/#comment-180711
Thu, 11 Oct 2012 01:34:57 +0000http://terrytao.wordpress.com/?p=6213#comment-180711Totally fascinating. Thanks for taking time to make notes on Weyl quantisation.
]]>By: degosson
https://terrytao.wordpress.com/2012/10/07/some-notes-on-weyl-quantisation/#comment-179995
Tue, 09 Oct 2012 11:22:20 +0000http://terrytao.wordpress.com/?p=6213#comment-179995Perhaps I missed something, but it seems that you don’t mention a characteristic property of Weyl pseudodifferential operators: they are the only members of the Shubin class that have the property of symplectic/metaplectic covariance (Stein, Wong) . Also, the fact that Weyl operators is the “perfect” quantization procedure in QM is debatable, as has been pointed out by many physicists. In view of Schwartz’s kernel theorem “everything” which is continuous S–>S’ can be written as a Weyl operator, hence any quantum observable could be “dequantized”, but this is physically not true: there are quantum observables which have no classical analogue. A better (i.e. more physical) quantization procedure might very well be the Born-Jordan scheme, which is not always “dequantizable” (see my latest paper “Symplectic covariance properties for Shubin and Born–Jordan pseudo-differential operators” in the Trans. Amer. Math. Soc, online since last Saturday: http://www.ams.org/journals/tran/0000-000-00/).
]]>By: Steven Stadnicki
https://terrytao.wordpress.com/2012/10/07/some-notes-on-weyl-quantisation/#comment-179801
Tue, 09 Oct 2012 00:52:21 +0000http://terrytao.wordpress.com/?p=6213#comment-179801Minor typo: your definition of the position operator is missing the factor of ; presumably it’s meant to be .

[Corrected, thanks – T.]

]]>By: Terence Tao
https://terrytao.wordpress.com/2012/10/07/some-notes-on-weyl-quantisation/#comment-179717
Mon, 08 Oct 2012 19:46:45 +0000http://terrytao.wordpress.com/?p=6213#comment-179717Yes, this would work, although for the purposes of Section 1, one could also proceed without the SL_2 invariance just by writing , and working with A’ and B’ throughout; this does not significantly affect the length of the presentation in this simple case, but is helpful when working with more than two variables as alluded to at the end of Section 1. To me it is a matter of taste – if one wants to prove some identity about finite-dimensional symplectic vector spaces, for instance, does one work in a coordinate free fashion, or does one apply the linear Darboux theorem first to place the symplectic form in a normal form? Both approaches are useful. (Of course, strictly speaking I did not work in a coordinate free fashion in my notes, since I did write everything in terms of A and B, but as mentioned above it is not too difficult to phrase things in the coordinate free formalism.)
]]>By: Anonymous
https://terrytao.wordpress.com/2012/10/07/some-notes-on-weyl-quantisation/#comment-179676
Mon, 08 Oct 2012 17:47:25 +0000http://terrytao.wordpress.com/?p=6213#comment-179676missing expository tag?
]]>