Supersymmetry in Quantum Theory Over a Galois Field

TL;DR

This paper demonstrates that a unique particle-antiparticle symmetry in Galois field quantum theory is compatible with supersymmetry, supporting the idea that this symmetry is fundamental in such theories and possibly in nature.

Contribution

It shows that the AB symmetry in Galois field quantum theory can coexist with supersymmetry, extending the understanding of symmetries in this framework.

Findings

AB symmetry is compatible with supersymmetry.

Parity properties of bosons and fermions follow from AB symmetry.

Supports the fundamental role of AB symmetry in GFQT.

Abstract

As shown in our previous papers (hep-th/0209001 and reference therein), quantum theory based on a Galois field (GFQT) possesses a new symmetry between particles and antiparticles, which has no analog in the standard approach. In the present paper it is shown that this symmetry (called the AB one) is also compatible with supersymmetry. We believe this is a strong argument in favor of our assumption that the AB symmetry is a fundamental symmetry in the GFQT (and in nature if it is described by quantum theory over a Galois field). We also consider operatorial formulations of space inversion and X inversion in the GFQT. It is shown in particular that the well known fact, that the parity of bosons is real and the parity of fermions is imaginary, is a simple consequence of the AB symmetry.