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

Insights Struggles with the Continuum - Part 4 - Comments

  1. Jan 25, 2016 #1

    john baez

    User Avatar
    Science Advisor
    Gold Member

    Last edited: Sep 6, 2016
  2. jcsd
  3. Jan 26, 2016 #2
    Really great series John!
     
  4. Jan 26, 2016 #3
    "PCT, Spin and Statistics, and All That" - I bought that little book when I was a student in the '60s. Never could make any sense of it. I felt especially bad since I was studying both statistics and physics and thought It should be within my grasp. But, I see with the wisdom of age (and John Baez's help) that I mainly had the wrong philosophical approach to the whole subject.
     
  5. Jan 27, 2016 #4
    I love this series.
     
  6. Jan 30, 2016 #5

    john baez

    User Avatar
    Science Advisor
    Gold Member

    It's a classic attempt to make quantum field theory mathematically rigorous, presenting the "Streater-Wightman axioms" for quantum fields as operator-valued distributions. However, that means you need to be comfortable with quantum field theory to enjoy this book!

    Maybe you'll feel better, if you don't already know this, to hear that the word "statistics" in this title has very little to do with statistics as practiced by statisticians. In quantum physics, "statistics" means the ways that identical particles transform when you permute them. There are two main possibilities: https://en.wikipedia.org/wiki/Bose–Einstein_statistics [Broken](for bosons) and Fhttps://en.wikipedia.org/wiki/Fermi–Dirac_statistics [Broken] (for fermions). The https://en.wikipedia.org/wiki/Spin–statistics_theorem [Broken] says that integer-spin particles must have Bose-Einstein statistics, while half-integer-spin particles must have Fermi-Dirac statistics.

    One of the triumphs of this book was to present a rigorous proof of the spin-statistics theorem for quantum fields obeying the Streater-Wightman axioms, along with another fundamental result called the PCT theorem, also known as the CPT theorem.
     
    Last edited by a moderator: May 7, 2017
  7. Jan 30, 2016 #6

    john baez

    User Avatar
    Science Advisor
    Gold Member

    Thanks! It looks like I need two more posts to cover quantum field theory without overwhelming people with mega-posts.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Struggles with the Continuum - Part 4 - Comments
  1. Independent Continuum (Replies: 8)

  2. Space Time Continuum (Replies: 4)

Loading...