Lifetimes

Dear Diary,


You see, Diary, we work in one dimension where some normal descriptions of matter break down.  We like one dimension because things are often easier to solve, but we need to be careful to avoid nasty physics (or hard math) that differs from problems we might want to solve in two or three dimensions.

One such instance is the description, known as a Fermi-liquid, that describes excitations that are close to the Fermi-surface very well in three dimensions (and two).  But if you try to calculate the quantum field properties in one dimension, you get a bad answer.  Specifically, the self-energy has a big imaginary part to it.  That's bad because it means the quasi-particles (or hypothetical weakly or non-interacting particles that would act like the many interacting particles) in our system have a short lifetime.  That means it's a bad description!  Ideally, we'd like the true quasi-particle that only weakly interacts in our system.  This means the math we wrote down to describe the system can be solved (perhaps more simply than the original problem if we find the right quasi-particle!).

For a real world example, let's describe how SCARY would tell the story of the camping trip last week.  A lot of that story would contain an untruthful description of the real events of that system that have a large imaginary part, but that means a made up story wouldn't have a very long lie-fetime!  One would say the made up quasi-particles in that system are a bad description of the actual events that happened.

You see, physics is useful for describing things.