Struggles with the Continuum - Part 4 - Comments

[john baez]

john baez submitted a new PF Insights post

Struggles with the Continuum - Part 4

Continue reading the Original PF Insights Post.

 

[Greg Bernhardt]

Really great series John!

 

[Steven Wenner]

"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.

 

[Jeff Rosenbury]

I love this series.

 

[john baez]

"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.

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!

I felt especially bad since I was studying both statistics and physics and thought It should be within my grasp.

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 (for bosons) and Fhttps://en.wikipedia.org/wiki/Fermi–Dirac_statistics (for fermions). The https://en.wikipedia.org/wiki/Spin–statistics_theorem 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.

 

[john baez]

Really great series John!

Thanks! It looks like I need two more posts to cover quantum field theory without overwhelming people with mega-posts.