# Contents

## Idea

The spectral action is a natural functional on the space of spectral triples.

Since a spectral triple encodes Riemannian geometry in a generalized context of noncommutative geometry, a functional on a space of spectral triples is comparable to the Einstein-Hilbert action functional on the space of ordinary Riemennian manifolds. And indeed, on spectral triples corresponding to ordinary Riemannian geometry the spectral action reduces to the Einstein-Hilbert action plus a series of integral over higher curvature invariants.

## Applications

The spectral action has been proposed as an action functional for describing fundamental physics. See at higher category theory and physics the section The standard model and gravity.

## References

The notion of spectral triple and of spectral action was introduced in

A discussion specifically of the spectral action is in

Earlier articles on this include

A claim that the spectral action for something like a 2-spectral triple does reproduce the effective background action of string theory is in

Revised on June 12, 2013 14:23:13 by Urs Schreiber (131.174.43.123)