# Generalization of Dirac conjugation in the superalgebraic theory of spinors

## TL;DR

This paper introduces a generalized Dirac conjugation within the superalgebraic framework of spinors, ensuring Lorentz covariance and preserving algebraic structures, advancing the mathematical understanding of spinor transformations.

## Contribution

It proposes a new form of Dirac conjugation in superalgebraic spinor theory that maintains Lorentz covariance and algebraic consistency.

## Key findings

- Generalized gamma matrices' signature and number are determined by the conjugation variant.
- Decomposition of second quantization by momenta aligns with the generalized conjugation.
- The CAR-algebra remains invariant under the new spinor transformations.

## Abstract

In the superalgebraic representation of spinors using Grassmann densities and derivatives with respect to them, a generalization of Dirac conjugation is introduced, which provides Lorentz-covariant transformations of conjugate spinors. It is shown that the signature of the generalized gamma matrices and their number, as well as the decomposition of the second quantization by momentums, are given by the variant of the generalized Dirac conjugation and by the requirement that the CAR-algebra be preserved in the transformations of the spinors and conjugate spinors.