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Do you have any interest in Quaternionic Quantum Mechanics?

  1. May 30, 2013 #1
    Do you have any interest in Quaternionic Quantum Mechanics?
    As far as i know, there are some people have interest in research a new formulation of quantum mechanics using quaternionic, rather than complex, numbers.''Quaternionic Quantum Mechanics and Quantum Fields'',by Stephen L. Adler ,who has been working on quaternionic quantum mechanics for the last fourteen years. The author clearly explicates the relations between quaternionic, complex and real quantum mechanics.And there are is a paper "The Quaternionic Quantum Mechanics" by Arbab I. Arbab (arXiv:1003.0075), but i personally think it is totally wrong,because he think of the quaternion as vector,but it's not so.
    Do you know any other Quaternionic Quantum Mechanics? If you know,please show it to me.
    By the way,who can tell me, where is the website can download the PDF document of “Quaternionic Quantum Mechanics and Quantum Fields" ,or if you have this document,please send to me {e-mail address removed} thanks
    Last edited by a moderator: May 31, 2013
  2. jcsd
  3. May 30, 2013 #2

    Simon Bridge

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    This guy?
    For his book you can always write and ask him? AFAIK: the book is still under copyright so a free download of the book would be illegal in most jurisditions.

    You are right - the quaternion is not a vector ... and it is not clear that it is an improvement on, say, matrix mechanics. Certainly if the aim is to avoid complex numbers in QM, it is a failure as it implicitly adds two extra independent complex variables to QM's one. OTOH the author seems to think it's worthwhile and he's been doing it longer than me.

    There are computational advantages to using quaternions in place of matrixes - especially for rotations - so they get used a lot in video games.
  4. May 31, 2013 #3
    It's possible to represent any qubit observable as a quaternion and any pure qubit state as a unit quaternion. Single-qubit QM can be written entirely in terms of quaternions without reference to state vectors, density matrices, or operators.

    I discovered this by accident working on my thesis, and I'm certainly not the first to notice. Qubit states and unitary transformations can be represented as points and rotations on the Bloch sphere, and quaternions can be used to represent 3D rotations.

    IMO, the unsolved question is whether there is any benefit to using quaternions instead of some other formalism. As Simon Bridge said, they do sometimes lead to very fast numerical methods. I have a hunch that multi-qubit simulations can be sped up by using hypercomplex numbers, but I ran out of time and money before I could come up with anything clear or useful on that topic.
  5. May 31, 2013 #4
    Are you an expert with quaternionic quantum mechanics ?
    and Stephen L. Adler ,is he a friend of yours?
  6. May 31, 2013 #5

    Simon Bridge

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    I do not know Steve personally, no.
    I like to take "expert" in two parts - the ex - which is a "used to be" and a "spurt" which is a drip working under pressure :D do not mistake me for any kind of authority.
  7. May 31, 2013 #6
    sorry,my English is poor,nevermind
  8. May 31, 2013 #7

    Simon Bridge

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    Sorry - that last sentence would be confusing to someone unfamiliar with English idiom.
    It's a pun inside another pun - if you google "drip under pressure" you will get a load of examples.
  9. May 31, 2013 #8
  10. May 31, 2013 #9


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    You can get a copy here, and they will even gift wrap it for you. :wink:

    Also, portions of it are available on Google Books.
  11. May 31, 2013 #10
    this book is too expensive for me:cry:
  12. Jun 1, 2013 #11
    sorry,i can't find it,Road to Reality
  13. Jun 1, 2013 #12
    Last edited by a moderator: May 6, 2017
  14. Jun 1, 2013 #13
    Last edited by a moderator: May 6, 2017
  15. Jun 1, 2013 #14
    by the way,what’s the meaning of “CW”? my English is poor,nevermind:biggrin:
  16. Jun 1, 2013 #15
    No, my English is poor!
    "CW" => Me! Charles Wilson
  17. Jun 1, 2013 #16
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