If Conley Zehnder index is known how one can use this information to compute the Maslov index and vice versa? Has somebody seen such calculations? Has somebody seen such calculations in the context of some quantum mechanical problems?
Thank you Remi. I know this paper but, it is too formal to be used effectively.Besides, the problem this time is not in chaoticity. The chinese guy used it for chaoticity only but, it should be applicable to just about any QM problem involving bound states and I am harboring the hope that somebody else also came to the same conclusion. So,I do not want to discover a wheel if the wheel is already discovered.
Hello Arkady,
I don't know if this will help, but the Keller-Maslov index is discussed in Kiyosi Itô's, Encyclopedic Dictionary of Mathematics, 2nd Ed., Volumes 1 & 2, MIT Press; 1985, Section 274 C (Vol. 1) - Fourier Integral Operators., which is part of Section 274 (Vol. 1) - Microlocal Analysis. There are two citations, [10] & [11], to the Keller-Maslov index on p. 1027 (Vol. 1):, but I think the first one is the one you want: [10] J. B. Keller; Corrected Bohr-Sommerfeld conditions for nonseparable systems; Ann. Phys. [Annals of Physics]; Vol. 4; [No. 2]; [June] 1958; pp. 180-188.
Regards,
Tom Cuff
Thomas, these are excellent references indeed.But I am talking about connections between the 2 indices. If you follow Remi's suggestion, then there should be such a connection. Thus, this is a research problem thus far.Which is good! Still I am cautious enough not to discover a wheel. The problem is interesting both mathematically and physically with far-far reaching implications
Hello Arkady,
Have you seen the 2007 paper by Maurice A. de Gosson at the following URL: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwjUrKaG9ufPAhXLHD4KHUE0AcMQFggcMAA&url=http%3A%2F%2Fwebdoc.sub.gwdg.de%2Febook%2Fserien%2Fe%2Fmpi_mathematik%2F2007%2F151.pdf&usg=AFQjCNGTNcM82kljOgfK8gpKyRy7EY3xwA ?
It is also available on ResearchGate and Academia, see the following URL: https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=%22keller-maslov%20index%22%20%22conley-zehnder%20index%22%20%22quantum%20mechanics
Regards,
Tom Cuff
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwjUrKaG9ufPAhXLHD4KHUE0AcMQFggcMAA&url=http%3A%2F%2Fwebdoc.sub.gwdg.de%2Febook%2Fserien%2Fe%2Fmpi_mathematik%2F2007%2F151.pdf&usg=AFQjCNGTNcM82kljOgfK8gpKyRy7EY3xwA
https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=%22keller-maslov%20index%22%20%22conley-zehnder%20index%22%20%22quantum%20mechanics
Tom, this (latest) citation is indeed helpful in the sense that it establishes a connection between 2 indices.I know works by Gosson in general but was not aware of this one in particular. Although I am capable of reading it, I still believe in existence of wider uses of the obtained results. Incidentally, Gosson himself was unable to find more applications of his own results as far as I can see things. Perhaps, knowing his work would make my efforts more reliable (since I can refer to the published work). My aim is to make physics community to be aware of the unexplored opportunities, especially in the light of papers like ER=EPR which are currently in vogue among physicists
I am M. de Gosson. The problem with these theories is that they are notoriously difficult to make accessible to non-specialists...If I can be of any help, please let me know...
Yes, Maurice you can and will be of enormous help. I like very much your works, especially your books. I am currently in Chicago where I am giving a talk at the U of Illinois at Chicago on subject matters VERY familiar to you.But this is only a gentle beginning.Much more work lies ahead and you are the most qualified person to be in touch with. So, I will. And very-very soon. Warmest regards,Arkady
Dear Arkady,
thank you for your kind answer. I am right now in Italy
Great, I am honored by your attention.We shall need to establish e-mail and skype connections in near future. Arkady
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