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Interacting fermions on non-commutative spaces: Exactly solvable quantum field theories in 2n+1 dimensions
KTH, Superseded Departments, Physics. KTH, School of Engineering Sciences (SCI). (Theoretical Physics)
2003 (English)In: Nuclear Physics B, ISSN 0550-3213, Vol. 654, no 3, 404-426 p.Article in journal (Refereed) Published
Abstract [en]

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.
Keyword [en]
grains, models
National Category
Natural Sciences
URN: urn:nbn:se:kth:diva-22374DOI: 10.1016/s0550-3213(03)00006-3ISI: 000181896100003OAI: diva2:341072
Swedish Research Council
QC 20100525 NR 20140804Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2012-02-13Bibliographically approved

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Langmann, Edwin
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