Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Insights Mathematical Quantum Field Theory - Spacetime - Comments

  1. Nov 7, 2017 #1

    Urs Schreiber

    User Avatar
    Science Advisor
    Gold Member

  2. jcsd
  3. Nov 7, 2017 #2

    jedishrfu

    Staff: Mentor

    Thanks for writing this excellent article.
     
  4. Nov 7, 2017 #3
    17 more parts to enjoy coming soon! :)
     
  5. Nov 8, 2017 #4

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    A minor note: Urs, I imagine you being more of a geometer than an analyst, so I would say: Relativistic field theory takes place on spacetime. ("on" in the exact sense of fiber bundle theory, in which the Minkowski spacetime - or a curved version of it - is the basis manifold of the fiber bundles which accommodate matter fields and gauge fields, thus, technically, one has fields "living" in their own spaces, not in spacetime.
    upload_2017-11-8_22-35-8.png
    Another note is that the metric tensor on the generic spacetime ##\eta## is nowhere explicitely defined as diag (-++...+) and the benefit of using it compared to the "West Coast" version diag (+--..-).
     
  6. Nov 8, 2017 #5

    strangerep

    User Avatar
    Science Advisor

    Typo in proof of example 2.23: "hatv".
     
  7. Nov 9, 2017 #6

    Urs Schreiber

    User Avatar
    Science Advisor
    Gold Member

    Thanks! Fixed now.
     
  8. Nov 9, 2017 #7

    Urs Schreiber

    User Avatar
    Science Advisor
    Gold Member

    Okay, I changed it. But I wasn't meaning to be speaking with any mathematical perspective at this point, but instead to first say something intuitive. I suppose we all feel that we live "in" spacetime, not "on" it. No?

    But anyway, I should not be using parenthetical remarks in an expositional paragraph. So I changed it to "on".

    I did say what the norm-square is supposed to be, but you are right that I never made explicit the induced Minkowski inner product. I have expanded now def. 2.15 to make it more explicit. Then I also added a remark 2.16 on how the metric encodes length and what this means for units of length (this will be needed later in chapter 5 to understand why mass terms come with the Compton wavelength.)

    Thanks for the feedback!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted