# Polarization spin-tensors in two-spinor formalism and Behrends-Fronsdal spin projection operator for $D$-dimensional case

## TL;DR

This paper derives differential relations linking polarization spin-tensors of free massive particles of arbitrary spin in four dimensions and introduces a new formula for the Behrends-Fronsdal spin projection operator in arbitrary dimensions.

## Contribution

It presents novel recurrent differential relations and a new formula for the Behrends-Fronsdal spin projection operator in D-dimensional space.

## Key findings

- Derived differential relations for polarization spin-tensors in 4D.
- Formulated a new D-dimensional Behrends-Fronsdal spin projection operator.
- Enhanced understanding of spin projection in higher-dimensional theories.

## Abstract

In the work, the recurrent differential relations that connecting the polarization spin-tensor of the wave function of a free massive particle of an arbitrary spin for $D=4$ and new formula of the $D$-dimensional Behrends-Fronsdal spin projection operator are found.