The quadratic spinor Lagrangian is equivalent to the teleparallel theory

TL;DR

This paper demonstrates that the quadratic spinor Lagrangian is equivalent to the teleparallel formulation of Einstein's theory, linking spinor-based and tetrad-based descriptions and aligning their energy-momentum definitions.

Contribution

It establishes the equivalence between the quadratic spinor Lagrangian and the teleparallel tetrad formulation of Einstein's theory, clarifying their relationship.

Findings

Quadratic spinor Lagrangian is equivalent to teleparallel gravity.

Energy-momentum density matches Moller's tensor from 1961.

Supports the spinor-tetrad correspondence in gravitational theories.

Abstract

The quadratic spinor Lagrangian is shown to be equivalent to the teleparallel / tetrad representation of Einstein's theory. An important consequence is that the energy-momentum density obtained from this quadratic spinor Lagrangian is essentially the same as the ``tensor'' proposed by Moller in 1961.