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The Spectrum of the Dirac Operator on the Hyperbolic Space
Author(s) -
Bunke Ulrich
Publication year - 1991
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19911530117
Subject(s) - dirac operator , mathematics , spinor , spectrum (functional analysis) , spin (aerodynamics) , dirac spinor , space (punctuation) , representation (politics) , mathematical physics , rank (graph theory) , homogeneous , operator (biology) , clifford analysis , hyperbolic space , pure mathematics , bundle , clifford bundle , mathematical analysis , dirac equation , combinatorics , quantum mechanics , physics , vector bundle , dirac algebra , normal bundle , computer science , materials science , repressor , law , chemistry , composite material , operating system , biochemistry , political science , transcription factor , thermodynamics , politics , gene , frame bundle
We represent the real hyperbolic space H n as the rank one homogeneous space Spin (1, n )/Spin ( n ) and the spinor bundle S of H as the homogeneous bundle Spin (1, n ) x Spin ( n ) V Δ where V Δ is the spinor representation space of Spin ( n ). The representation theoretic decomposition of L 2 ( H, S ) combined with the PARTHASARATHY formula for the DIRAC operator D yields the spectral representation of D 2 .
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