Spectral asymmetry on the ball and asymptotics of the asymmetry kernel

Details Spectral asymmetry on the ball and asymptotics of the asymmetry kernel Spectral asymmetry on the ball and asymptotics of the asymmetry kernel

2006-05-05

arxiv.org/abs/hep-th/0605067v1

J.Phys.A39:9573-9589,2006

Physics

High Energy Physics

High Energy Physics - Theory

23 pages

Scientific paper

10.1088/0305-4470/39/30/012

Let $\ui\di$ be the Dirac operator on a $D=2d$ dimensional ball $\mcB$ with radius $R$. We calculate the spectral asymmetry $\eta(0,\ui\di)$ for D=2 and D=4, when local chiral bag boundary conditions are imposed. With these boundary conditions, we also analyze the small-$t$ asymptotics of the heat trace $\Tr (F P e^{-t P^2})$ where $P$ is an operator of Dirac type and $F$ is an auxiliary smooth smearing function.

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