Global boundary conditions for the Dirac operator

Details Global boundary conditions for the Dirac operator Global boundary conditions for the Dirac operator

1997-05-12

arxiv.org/abs/physics/9705013v1

Physics

Mathematical Physics

13 pages, RevTeX. Talk given at the Trends in Theoretical Physics, CERN - Santiago de Compostela - La Plata Meeting, April 27

Scientific paper

10.1063/1.54693

Ellipticity of boundary value problems is characterized in terms of the Calderon projector. The presence of topological obstructions for the chiral Dirac operator under local boundary conditions in even dimension is discussed. Functional determinants for Dirac operators on manifolds with boundary are considered. The functional determinant for a Dirac operator on a bidimensional disk, in the presence of an Abelian gauge field and subject to global boundary conditions of the type introduced by Atiyah-Patodi-Singer, is evaluated. The relationship with the index theorem is also commented.

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