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[en] We start from the Dirac operator for the Coulomb potential and prove within first order perturbation theory that degenerate levels split in a definite way depending on the sign of the Laplacian of the perturbing potential. 9 refs. (Author)

[en] Functions p(x) and q(x) for which the Dirac operator has a countable number of eigenvalues in the continuous spectrum are constructed

[en] A rapid algorithm for calculating γ-matrix traces in frames of analytical calculation system REDUCE is described. Algorithms consist in sequential application of Firtz identities. As a result from a graph representing initial trace of Dirac matrices the graph, on which basis algebraic equation is unambigously retored, is produced. Results of comparing operation of REDUCE system high energy packet and realized by authors Kennedy-Tsvitanovich algorithm are presented graphically. 3 refs.; 1 fig

[en] In this paper, the spectral action for the free Dirac operator on a fuzzy 2-sphere is considered, based on the known results. We show that from the spectral point of view, the behavior of the fuzzy sphere can be divided into three regimes: the classical regime, the quasi-classical regime and the fuzzy regime. We also consider its application to quantum cosmology.

[en] We consider Dirac operators on odd-dimensional compact spin manifolds which are twisted by a product bundle. We show that the space of connections on the twisting bundle which yields an invertible operator has infinitely many connected components if the untwisted Dirac operator is invertible and the dimension of the twisting bundle is sufficiently large

[en] The relation between complex line bundles and certain group cocycles is explored in general to obtain explicit formulae for the transition functions and curvature of the determinant line bundle DET of a family of Dirac operators coupled to Yang-Mills fields. A covariant derivative on sections of DET is constructed which realizes the curvature and 'minimally couples' to the integrated anomaly which thus appears as a 'functional magnetic field' on gauge orbit space. The transcription of group cohomological (cocycles) into geometrical (line bundles) information is refined in such a way that the relevant cohomology groups can be computed in many cases, giving insight into the classification of lifts of principal group actions. 23 refs. (Author)

[en] The spectral properties of Dirac operators with singular potentials that are constructed by means of a cut-off procedure are investigated. The invariance of the essential spectrum is proved, norm resolvent convergence of the cut-off operators is established and spectral gap formulas are proved

[en] Some general remarks about dimensional regularization are offered. Then we show that among the schemes so far proposed for theories involving γ₅ and (or) epsilonsub(μ)sub(ν)sub(p)sub(sigma) only the original one with a non-anticommuting γ₅ is consistent. (orig.)

[en] It is shown, how - in the setting of Clifford bundles - the spin connection (or Dirac operator) may be obtained by averaging the Levi-Civita connection (or Kaehler-Dirac operator) over the finite group generated by an orthonormal frame of the base-manifold. The familiar covariance of the Dirac equation under a simultaneous transformation of spinors and matrix-representations emerges very naturally in this scheme, which can also be applied when the manifold does not possess a spin-structure. (Author)