Self-Dual Conformal Supergravity and the Hamiltonian Formulation

TL;DR

This paper develops a Hamiltonian formulation of self-dual conformal supergravity using Dirac matrices, focusing on the Ashtekar connection as a fundamental variable, and derives the associated constraints.

Contribution

It introduces a connection dynamic theory of self-dual conformal supergravity with a Hamiltonian framework based on the Ashtekar connection, expanding the understanding of supergravity formulations.

Findings

Formulation of self-dual conformal supergravity using Dirac matrices.

Derivation of Hamiltonian and constraints via Dirac-Bergmann algorithm.

Identification of the Ashtekar connection as a key dynamic variable.

Abstract

In terms of Dirac matrices the self-dual and anti-self-dual decomposition of a conformal supergravity is given and a self-dual conformal supergravity theory is developed as a connection dynamic theory in which the basic dynamic variabes include the self-dual spin connection i.e. the Ashtekar connection rather than the triad. The Hamiltonian formulation and the constraints are obtained by using the Dirac-Bergmann algorithm. PACS numbers: 04.20.Cv, 04.20.Fy,04.65.+e