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Ray vs vector

  1. Feb 12, 2009 #1
    Hello,

    I am reading Weinberg's book and in the part on symmetries he speaks about rays, and says basically that 2 vectors [tex]U,V[/tex] which are on the same ray can only differ by a phase factor [tex]\phi[/tex], so that [tex]U=e^{i\phi}V[/tex].

    Is "ray" meaning "direction" here ? Can I rephrase it and say that 2 colinear vectors can only differ by a phase factor ?

    Thanks for your help!
     
  2. jcsd
  3. Feb 12, 2009 #2

    tiny-tim

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    Hi emma! :smile:

    From pp. 49-50:
    So a ray is an equivalence class of normalised vectors in Hilbert space …

    two normalised vectors "are" the same ray if they only differ by a phase factor. :smile:

    (but i don't think thinking in terms of "directions" is helpful, when these things are more like functions :wink:)
     
  4. Feb 12, 2009 #3
    Thank your very much!

    Ok, now I think I also understand why he infers [tex]e^{i\phi}[/tex] as proportional factor (and not just e.g. a [tex]k \in \mathbb{C}[/tex]) between the 2 vectors: because it is the most general complex proportional factor which is normalized to 1...
     
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