# A note on Duffin-Kemmer-Petiau equation in (1+1) space-time dimensions

## TL;DR

This paper clarifies that in (1+1) dimensions, the Duffin-Kemmer-Petiau algebra only admits a spin-0 representation, challenging previous assumptions about the spin-1 sector in this reduced dimensionality.

## Contribution

It explicitly demonstrates that the DKP algebra in (1+1) dimensions admits only a spin-0 representation, clarifying misconceptions about the spin-1 sector in lower dimensions.

## Key findings

- DKP algebra in (1+1) dimensions admits only spin-0 representation
- Clarifies why previous studies found similar results for spin-0 and spin-1 sectors in reduced dimensions
- Provides insight into the structure of DKP theory in lower-dimensional space-times

## Abstract

In the last years several papers addressed the supposed spin-1 sector of the massive Duffin-Kemmer-Petiau (DKP) equation restricted to (1+1) space-time dimensions. In this note we show explicitly that this is a misleading approach, since the DKP algebra in (1+1) dimensions admits only a spin-0 representation. Our result also is useful to understand why several recent papers found coincident results for both spin-0 and spin-1 sectors of the DKP theory in (3+1) dimensions when the dynamics is restricted to one space dimension.