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SPECTRAL METRIC AND EINSTEIN FUNCTIONALS
- Speaker(s)
- LUDWIK DĄBROWSKI
- Affiliation
- SISSA
- Date
- Nov. 16, 2022, 5:15 p.m.
- Information about the event
- 405 IMPAN & ZOOM
- Seminar
- North Atlantic Noncommutative Geometry Seminar
Using the Wodzicki residue, in terms of the Laplace operator, we define two bilinear functionals on vector fields. Their densities yield, respectively, the metric tensor and the Einstein tensor on an even-dimensional Riemannian manifold. Then, in terms of the Dirac operator, we define two bilinear functionals on differential forms. Their densities, in turn, yield the contravariant metric tensor and the Einstein tensor on an even-dimensional spin manifold, respectively. We generalise these concepts to non-commutative geometry. In particular, we prove that the Einstein functional vanishes for the conformally rescaled geometry of the noncommutative two-torus.
