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<https://discovery.ucl.ac.uk/id/eprint/1498494> <http://purl.org/dc/terms/title> "Spectral analysis of the Dirac operator on a 3-sphere"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/1498494> <http://purl.org/ontology/bibo/abstract> "We study the (massless) Dirac operator on a 3-sphere equipped with Riemannian metric. For\r\nthe standard metric the spectrum is known. In particular, the eigenvalues closest to zero are the\r\ntwo double eigenvalues +3/2 and −3/2. Our aim is to analyse the behaviour of eigenvalues when\r\nthe metric is perturbed in an arbitrary smooth fashion from the standard one. We derive explicit\r\nperturbation formulae for the two eigenvalues closest to zero, taking account of the second variations.\r\nNote that these eigenvalues remain double eigenvalues under perturbations of the metric:\r\nthey cannot split because of a particular symmetry of the Dirac operator in dimension three\r\n(it commutes with the antilinear operator of charge conjugation). Our perturbation formulae\r\nshow that in the first approximation our two eigenvalues maintain symmetry about zero and are\r\ncompletely determined by the increment of Riemannian volume. Spectral asymmetry is observed\r\nonly in the second approximation of the perturbation process. As an example we consider a\r\nspecial family of metrics, the so-called generalized Berger spheres, for which the eigenvalues can\r\nbe evaluated explicitly."^^<http://www.w3.org/2001/XMLSchema#string> .
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