Abstract
We study the relations between different determinants of the Dirac operator over a manifold with boundary considered as sections of a holomorphic line bundle over the Grassmannian of boundary conditions of Atiyah–Patodi–Singer type.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Atiyah, M. F.: Topological quantum field theories, Publ. Math. IHES 68 (1989), 175–186.
Atiyah, M. F., Patodi, V. K. and Singer, I. M.: Spectral asymmetry and Riemannian geometry I, III, Math. Proc. Cambridge Philos. Soc. 77 (1975), 43–69; 79 (1976), 71–99.
Bismut, J.-M. and Cheeger, J.: Families index for manifolds with boundary, superconnections and cones I, II, J. Funct. Anal. 89 (1990), 313–363; 90 (1990), 306–354.
Bismut, J.-M. and Freed, D.: The analysis of elliptic families I, II, Comm. Math. Phys. 106 (1986), 159–176; 107 (1986), 103–163.
Booss-Bavnbek, B. and Wojciechowski, K. P.: Pseudodifferential projections and the topology of certain spaces of elliptic boundary value problems, Comm. Math. Phys. 121 (1989), 1–9.
Booss-Bavnbek, B. and Wojciechowski, K. P.: Elliptic Boundary Problems for Dirac Operators, Birkhäuser, Boston, 1993.
Dai, X. and Freed, D.: η-invariants and determinant lines, J. Math. Phys. 35 (1994), 5155–5195.
Douglas, R. G. and Wojciechowski, K. P.: Adiabatic limits of the η-invariants. The odd dimensional Atiyah–Patodi–Singer problem, Comm. Math. Phys. 142 (1991), 139–168.
Klimek, S. and Wojciechowski, K. P.: Adiabatic cobordism theorems for analytic torsion and η-invariant, J. Funct. Anal. 136 (1996), 269–293.
Lesch, M. and Wojciechowski, K. P.: On the η-invariant of generalized Atiyah–Patodi–Singer problems, Illinois J. Math. 40 (1996), 30–46.
Melrose, R. B. and Piazza, P.: Families of Dirac operators, boundaries and the b-calculus, Preprint, 1993.
Pressley, A. and Segal, G. B.: Loop Groups, Oxford University Press, Oxford, 1986.
Quillen, D.: Determinants of Cauchy–Riemann operators over a Riemann surface, Funct. Anal. Appl. 19 (1985), 31–34.
Scott, S. G.: Determinants of Dirac boundary value problems over odd-dimensional manifolds, Comm. Math. Phys. 173 (1995), 43–76.
Scott, S. G. and Wojciechowski, K. P.: Determinants and Grassmannians, in preparation.
Segal, G. B.: The definition of conformal field theory, Preprint, 1993.
Singer, I. M.: Families of Dirac operators with applications to physics, Asterisque, hors serie, (1985), pp. 323–340.
Witten, E.: Quantum field theory, Grassmannians, and algebraic curves, Comm. Math. Phys. 113 (1988), 529–600.
Witten, E.: Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1988), 351–399.
Wojciechowski, K. P.:On the additivity of the η-invariant. The case of singular tangential operator, Comm. Math. Phys. 169 (1995), 315–327.
Wojciechowski, K. P.: Smooth, self-adjoint Grassmannian, The η-invariant, and ζ-determinant of boundary problems, Preprint, 1996.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Scott, S.G., Wojciechowski, K.P. Determinants, Grassmanniannians and Elliptic Boundary Problems for the Dirac Operator. Letters in Mathematical Physics 40, 135–145 (1997). https://doi.org/10.1023/A:1007391620108
Issue Date:
DOI: https://doi.org/10.1023/A:1007391620108