TY  - JOUR
SN  - 1846-3886
N1  - This version is the author accepted manuscript. For information on re-use, please refer to the publisher?s terms and conditions.
ID  - discovery1498494
AV  - public
EP  - 527
JF  - Operators and Matrices
N2  - We study the (massless) Dirac operator on a 3-sphere equipped with Riemannian metric. For
the standard metric the spectrum is known. In particular, the eigenvalues closest to zero are the
two double eigenvalues +3/2 and ?3/2. Our aim is to analyse the behaviour of eigenvalues when
the metric is perturbed in an arbitrary smooth fashion from the standard one. We derive explicit
perturbation formulae for the two eigenvalues closest to zero, taking account of the second variations.
Note that these eigenvalues remain double eigenvalues under perturbations of the metric:
they cannot split because of a particular symmetry of the Dirac operator in dimension three
(it commutes with the antilinear operator of charge conjugation). Our perturbation formulae
show that in the first approximation our two eigenvalues maintain symmetry about zero and are
completely determined by the increment of Riemannian volume. Spectral asymmetry is observed
only in the second approximation of the perturbation process. As an example we consider a
special family of metrics, the so-called generalized Berger spheres, for which the eigenvalues can
be evaluated explicitly.
VL  - 12
SP  - 501
UR  - http://dx.doi.org/10.7153/oam-2018-12-31
TI  - Spectral analysis of the Dirac operator on a 3-sphere
KW  - Science & Technology
KW  -  Physical Sciences
KW  -  Mathematics
KW  -  Dirac operator
KW  -  spectral asymmetry
KW  -  generalized Berger spheres
KW  -  RIEMANNIAN GEOMETRY
KW  -  THEORETIC CHARACTERIZATION
KW  -  1ST-ORDER SYSTEMS
KW  -  HARMONIC SPINORS
KW  -  ASYMMETRY
IS  - 2
A1  - Fang, Y-L
A1  - Levitin, M
A1  - Vassiliev, D
PB  - ELEMENT
Y1  - 2018/06/01/
ER  -