Quantum statistical mechanics over function fields

Details Quantum statistical mechanics over function fields Quantum statistical mechanics over function fields

2006-07-15

arxiv.org/abs/math/0607363v2

Mathematics

Quantum Algebra

28 pages, LaTeX; v2: last section expanded

Scientific paper

In this paper we construct a noncommutative space of ``pointed Drinfeld modules'' that generalizes to the case of function fields the noncommutative spaces of commensurability classes of Q-lattices. It extends the usual moduli spaces of Drinfeld modules to possibly degenerate level structures. In the second part of the paper we develop some notions of quantum statistical mechanics in positive characteristic and we show that, in the case of Drinfeld modules of rank one, there is a natural time evolution on the associated noncommutative space, which is closely related to the positive characteristic L-functions introduced by Goss. The points of the usual moduli space of Drinfeld modules define KMS functionals for this time evolution. We also show that the scaling action on the dual system is induced by a Frobenius action, up to a Wick rotation to imaginary time.

Affiliated with

Also associated with

No associations

Rating

Quantum statistical mechanics over function fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quantum statistical mechanics over function fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum statistical mechanics over function fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-331432