Thermofield dynamics and Gravity

TL;DR

This paper explores thermofield dynamics through path-integral and coadjoint orbit methods, proposing a novel approach to formulating gravitational dynamics in noncommutative geometry by doubling the Hilbert space, with detailed analysis in 2+1 dimensions.

Contribution

It introduces a new formulation of thermofield dynamics using path-integrals and extends it to noncommutative gravity via doubled Hilbert spaces, connecting to Einstein-Hilbert action in the commutative limit.

Findings

Thermofield dynamics can be expressed via path-integral and coadjoint orbit actions.

A field theoretic formulation on a doubled manifold is developed.

In 2+1 dimensions, the gravitational action emerges as a difference of Chern-Simons actions.

Abstract

Thermofield dynamics is presented in terms of a path-integral using coherent states, equivalently, using a coadjoint orbit action. A field theoretic formulation in terms of fields on a manifold ${\mathcal M} \times {\tilde{\mathcal M}}$ where the two components have opposite orientation is also presented. We propose formulating gravitational dynamics for noncommutative geometry using thermofield dynamics, doubling the Hilbert space modeling the noncommutative space. We consider 2+1 dimensions in some detail and since ${\mathcal M}$ and ${\tilde{\mathcal M}}$ have opposite orientation, the commutative limit leads to the Einstein-Hilbert action as the difference of two Chern-Simons actions.