The spectrum of the Dirac operator on coset spaces with homogeneous gauge fields | Zendy

Brian P. Dolan | Zendy

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The spectrum of the Dirac operator on coset spaces with homogeneous gauge fields

Author(s) -

Brian P. Dolan

Publication year - 2003

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2003/05/018

Subject(s) - homogeneous space , dirac operator , coset , mathematical physics , spectrum (functional analysis) , degeneracy (biology) , homogeneous , operator (biology) , space (punctuation) , atiyah–singer index theorem , connection (principal bundle) , physics , gauge theory , field (mathematics) , mathematics , quantum mechanics , pure mathematics , discrete mathematics , biochemistry , chemistry , geometry , repressor , gene , transcription factor , bioinformatics , linguistics , philosophy , biology , thermodynamics

The spectrum and degeneracies of the Dirac operator are analysed on compactcoset spaces when there is a non-zero homogeneous background gauge field whichis compatible with the symmetries of the space, in particular when the gaugefield is derived from the spin-connection. It is shown how the degeneracy ofthe lowest Landau level in the recently proposed higher dimensional quantumHall effect is related to the Atiyah-Singer index theorem for the Diracoperator on a compact coset space.Comment: 25 pages, typeset in LaTeX, uses youngtab.st

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