Topological Calculation of the Phase of the Determinant of a Non Self-adjoint Elliptic Operator

@inproceedings{Abanov2004TopologicalCO,
  title={Topological Calculation of the Phase of the Determinant of a Non Self-adjoint Elliptic Operator},
  author={Alexander G. Abanov and M Kappeler Braverman},
  year={2004}
}
We study the zeta-regularized determinant of a non self-adjoint elliptic operator on a closed odd-dimensional manifold. We show that, if the spectrum of the operator is symmetric with respect to the imaginary axis, then the determinant is real and its sign is determined by the parity of the number of the eigenvalues of the operator, which lie on the positive part of the imaginary axis. It follows that, for many geometrically defined operators, the phase of the determinant is a topological… CONTINUE READING

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References

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Showing 1-10 of 14 references

Complex powers of elliptic operators

  • R. Seeley
  • Proc. Symp. Pure and Appl. Math. AMS 10
  • 1967
Highly Influential
5 Excerpts

Theta-terms in nonlinear sigma-models

  • A. G. Abanov, P. B. Wiegmann
  • Nucl.Phys. B570
  • 2000
Highly Influential
6 Excerpts

Heat equation and spectral geometry

  • K. P. Wojciechowski
  • Introduction for beginners, Geometric methods for…
  • 1999

Hilbert space: compact operators and the trace theorem

  • J. R. Retherford
  • London Mathematical Society Student Texts, vol…
  • 1993

On the determinant of elliptic differential and finite difference operators in vector bundles over S1

  • D. Burghelea, L. Friedlander, T. Kappeler
  • Comm. Math. Phys. 138
  • 1991
1 Excerpt

Elliptic operators on closed manifolds

  • M. S. Agranovich
  • Current problems in mathematics. Fundamental…
  • 1990

Gauge Noninvariance and Parity Nonconservation of Three-Dimensional Fermions

  • A. N. Redlich
  • Phys. Rev. Lett. 52,
  • 1984

Local invariants of spectral asymmetry

  • M. Wodzicki
  • Invent. Math. 75
  • 1984

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