Essential Self-Adjointness and Invariance of the Essential Spectrum for Dirac Operators | Zendy

Masaharu Arai | Zendy; Osanobu Yamada | Zendy

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Essential Self-Adjointness and Invariance of the Essential Spectrum for Dirac Operators

Author(s) -

Masaharu Arai,

Osanobu Yamada

Publication year - 1982

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195183289

Subject(s) - hermitian matrix , mathematics , mathematical physics , spectrum (functional analysis) , hilbert space , dirac operator , matrix (chemical analysis) , self adjoint operator , pure mathematics , dirac (video compression format) , norm (philosophy) , mathematical analysis , quantum mechanics , physics , materials science , composite material , political science , law , neutrino

where «_,(j = 1, 2, 3) and a4 = /? are Hermitian symmetric, constant, 4x4 matrices and satisfy the anti-commutation relations (U) aLjQik + aikaij = 2djkI (/, k = l, 2, 3, 4) (/ is the 4x4 unit matrix). Throughout this paper the potential Q(x) is assumed to be an Hermitian symmetric 4x4 matrix-valued measurable function. The Dirac operator is treated in the Hilbert space ^ = [L(U)] associated with the norm

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