Determinants, Grassmannians and Elliptic Boundary Problems for the Dirac Operator

Letters in Mathematical Physics

Volumn 40, Issue 2, 1977, Pages 135-145

  Scott, Simon G ^a   Wojciechowski, Krzysztof P ^b  

^a UNIVERSIDAD DE LOS ANDES   (Colombia)

^b INDIANA UNIVERSITY   (United States)

Author keywords

Atiyah Patodi Singer condition; Calderon projection; Canonical determinant; Dirac operator; Grassmannian of boundary conditions; Quillen determinant; determinant

Indexed keywords

EID: 0008989461     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007391620108     Document Type: Article

References (24)

1. Atiyah, M. F.: Topological quantum field theories, Publ. Math. IHES 68 (1989), 175-186.
2. 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.
3. 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.
4. 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.
5. 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.
6. Bismut, J.-M. and Freed, D.: The analysis of elliptic families I, II, Comm. Math. Phys. 106 (1986), 159-176; 107 (1986), 103-163.
7. Bismut, J.-M. and Freed, D.: The analysis of elliptic families I, II, Comm. Math. Phys. 106 (1986), 159-176; 107 (1986), 103-163.
8. 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.
9. Booss-Bavnbek, B. and Wojciechowski, K. P.: Elliptic Boundary Problems for Dirac Operators, Birkhäuser, Boston, 1993.
10. Dai, X. and Freed, D.: η-invariants and determinant lines, J. Math. Phys. 35 (1994), 5155-5195.
11. 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.
12. Klimek, S. and Wojciechowski, K. P.: Adiabatic cobordism theorems for analytic torsion and η-invariant, J. Funct. Anal. 136 (1996), 269-293.
13. Lesch, M. and Wojciechowski, K. P.: On the η-invariant of generalized Atiyah-Patodi-Singer problems, Illinois J. Math. 40 (1996), 30-46.
14. Melrose, R. B. and Piazza, P.: Families of Dirac operators, boundaries and the b-calculus, Preprint, 1993.
15. Pressley, A. and Segal, G. B.: Loop Groups, Oxford University Press, Oxford, 1986.
16. Quillen, D.: Determinants of Cauchy-Riemann operators over a Riemann surface, Funct. Anal. Appl. 19 (1985), 31-34.
17. Scott, S. G.: Determinants of Dirac boundary value problems over odd-dimensional manifolds, Comm. Math. Phys. 173 (1995), 43-76.
18. Scott, S. G. and Wojciechowski, K. P.: Determinants and Grassmannians, in preparation.
19. Segal, G. B.: The definition of conformal field theory, Preprint, 1993.
20. Singer, I. M.: Families of Dirac operators with applications to physics, Asterisque, hors serie, (1985), pp. 323-340.
21. Witten, E.: Quantum field theory, Grassmannians, and algebraic curves, Comm. Math. Phys. 113 (1988), 529-600.
22. Witten, E.: Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1988), 351-399.
23. Wojciechowski, K. P.: On the additivity of the η-invariant. The case of singular tangential operator, Comm. Math. Phys. 169 (1995), 315-327.
24. Wojciechowski, K. P.: Smooth, self-adjoint Grassmannian, The η-invariant, and ζ-determinant of boundary problems, Preprint, 1996.