Interacting fermions on non-commutative spaces: Exactly solvable quantum field theories in 2n+1 dimensions
2003 (English)In: Nuclear Physics B, ISSN 0550-3213, Vol. 654, no 3, 404-426 p.Article in journal (Refereed) Published
I present a novel class of exactly solvable quantum field theories. They describe non-relativistic fermions on even-dimensional flat space, coupled to a constant external magnetic field and a four point interaction defined with the Groenewold-Moyal star product. Using Hamiltonian quantization and a suitable regularization, I show that these models have a dynamical symmetry corresponding to gl(infinity) circle plus gl(infinity) at the special points Btheta = I and Btheta = -I, where B and theta are the matrices defining the magnetic field and the star product, respectively. I construct all eigenvalues and eigenstates, of the many-body Hamiltonian at these special points. I argue that this solution cannot be obtained by any mean-field theory, i.e., the models describe correlated fermions. I also mention other possible interpretations of these models in solid state physics.
Place, publisher, year, edition, pages
Elsevier, 2003. Vol. 654, no 3, 404-426 p.
IdentifiersURN: urn:nbn:se:kth:diva-22374DOI: 10.1016/s0550-3213(03)00006-3ISI: 000181896100003OAI: oai:DiVA.org:kth-22374DiVA: diva2:341072
FunderSwedish Research Council
QC 20100525 NR 201408042010-08-102010-08-102012-02-13Bibliographically approved