# On the Spinor Representation

## TL;DR

This paper systematically studies the spinor representation using fermionic physical space, revealing its geometric and topological structure and the constraints imposed by Fierz-Pauli-Kofink identities on spinor bilinear covariants.

## Contribution

It provides a comprehensive analysis of the spinor representation space, highlighting its geometric, topological features, and the role of identities in constraining the space.

## Key findings

- Spinor space is constrained by Fierz-Pauli-Kofink identities.
- The spinor space exhibits a rich geometric and topological structure.
- Homotopy groups influence physical properties of fermionic fields.

## Abstract

A systematic study of the spinor representation by means of the fermionic physical space is accomplished and implemented. The spinor representation space is shown to be constrained by the Fierz-Pauli-Kofink identities among the spinor bilinear covariants. A robust geometric and topological structure can be manifested from the spinor space, wherein, for instance, the first and second homotopy groups play prominent roles on the underlying physical properties, associated to the fermionic fields.