Arcadian Functor

occasional meanderings in physics' brave new world

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Marni D. Sheppeard

Sunday, August 31, 2008

Mass Gap Revisited

Woit points to some new talks (not online, unfortunately) about the Mass Gap problem. Apparently Witten discussed this problem from a non-Abelian Hamiltonian point of view, and nicely avoided gauge symmetries even though the term Gauge Theory appears in the title of the talk.

Anyway, Carl has also been bugging me a bit about Hamiltonians. Honestly, I wish we could move beyond 19th century physics, but perhaps it is useful to think about what a Hamiltonian operator should be from a categorical viewpoint. To begin with, Vicary's paper is a must read, defining the harmonic oscillator entirely in categorical terms.

Let us say that a Hamiltonian is any operator sitting in an eigenvalue equation for states associated with mass-energy. Hmmmmm.


Blogger CarlBrannen said...


What I don't like about the mass gap problem is that I think it's wrong in that it's stated in terms of the quantum vacuum.

The quantum vacuum only exists in quantum field theory, it does not exist in quantum mechanics. QFT needs a vacuum because they have to have a states for every number of particles that might exist, and so the vacuum is the state with zero particles.

The vacuum, as a mathematical concept, disappears when you write things in measurement algebra. It also melts away when you convert things to density operators.

The basic problem is that the vacuum is a state, and as such, it is not an operator. I'd rather work in a language where the states are operators, and all results can be written as relationships between operators.

I'm working on the "statistics" part of the mass paper now. Things are moving along, but this is long dull work.

August 31, 2008 2:26 PM  
Blogger Kea said...

Carl, of course I agree that the problem is ill posed, as I'm sure I've said before. But we can still talk about Mass Gaps!

August 31, 2008 5:55 PM  

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