The zeta-determinants of Dirac Laplacians with boundary conditions on the smooth, self-adjoint Grassmannian
- 作者：Yoonweon Lee
- 关键词：Zeta- and relative zeta-determinants ; BFK-gluing formula ; Dirichlet and APS boundary conditions ; Smooth self-adjoint Grassmannian ; Calderó ; n projector
- 刊名：Journal of Geometry and Physics
- 出版年：2007
- 期刊代码：29_03930440
- 类别：ph
- 出版时间：September 2007
- 卷：57
- 期：10
- 页码：1951-1976
- 文件大小：444 K
摘要
In this paper we describe the difference of log of two zeta-determinants of Dirac Laplacians subject to the Dirichlet boundary condition and a boundary condition on the smooth, self-adjoint Grassmannian 
on a compact manifold with boundary. Using this result we obtain the result of Scott and Wojciechowski [S.G. Scott, Zeta determinants on manifolds with boundary, J. Funct. Anal. 192 (2002) 112–185; S.G. Scott, K.P. Wojciechowski, The ζ-determinant and Quillen determinant for a Dirac operator on a manifold with boundary, Geom. Funct. Anal. 10 (2000) 1202–1236] concerning the quotient of two zeta-determinants of Dirac Laplacians with boundary conditions on 
. We apply these results to the BFK-gluing formula to obtain the gluing formula for the zeta-determinants of Dirac Laplacians with respect to boundary conditions on 
. We next discuss the zeta-determinants of Dirac Laplacians subject to the Dirichlet or APS boundary condition on a finite cylinder and finally discuss the relative zeta-determinant on a manifold with cylindrical end when the APS boundary condition is imposed on the bottom of the cylinder.