The chiral determinant and the eta invariant

S. Della Pietra; V. Della Pietra; L. Alvarez-Gaumé

doi:10.1007/BF01208963

The chiral determinant and the eta invariant

S. Della Pietra
, V. Della Pietra
, L. Alvarez-Gaumé

Simons Center for Geometry & Physics

Harvard University
University of Texas at Austin

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

Abstract

For {∂_y}, yε∈, a one parameter family of invertible Weyl operators of possibly non-zero index acting on spinors over an even dimensional compact manifold X, we express the phase of the chiral determinant det ∂_-∞^† ∂_∞ in terms of the η invariant of a Dirac operator acting on spinors over ℝ ×X.

Original language	English
Pages (from-to)	691-700
Number of pages	10
Journal	Communications in Mathematical Physics
Volume	109
Issue number	4
DOIs	https://doi.org/10.1007/BF01208963
State	Published - Dec 1987

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title = "The chiral determinant and the eta invariant",

abstract = "For \{∂y\}, yε∈, a one parameter family of invertible Weyl operators of possibly non-zero index acting on spinors over an even dimensional compact manifold X, we express the phase of the chiral determinant det ∂-∞† ∂∞ in terms of the η invariant of a Dirac operator acting on spinors over ℝ ×X.",

author = "\{Della Pietra\}, S. and \{Della Pietra\}, V. and L. Alvarez-Gaum{\'e}",

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AU - Della Pietra, S.

AU - Della Pietra, V.

AU - Alvarez-Gaumé, L.

PY - 1987/12

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N2 - For {∂y}, yε∈, a one parameter family of invertible Weyl operators of possibly non-zero index acting on spinors over an even dimensional compact manifold X, we express the phase of the chiral determinant det ∂-∞† ∂∞ in terms of the η invariant of a Dirac operator acting on spinors over ℝ ×X.

AB - For {∂y}, yε∈, a one parameter family of invertible Weyl operators of possibly non-zero index acting on spinors over an even dimensional compact manifold X, we express the phase of the chiral determinant det ∂-∞† ∂∞ in terms of the η invariant of a Dirac operator acting on spinors over ℝ ×X.

UR - https://www.scopus.com/pages/publications/0002085588

U2 - 10.1007/BF01208963

DO - 10.1007/BF01208963

M3 - Article

AN - SCOPUS:0002085588

SN - 0010-3616

VL - 109

SP - 691

EP - 700

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 4

ER -

The chiral determinant and the eta invariant

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