Duffin–Kemmer–Petiau algebra

In mathematical physics, the Duffin–Kemmer–Petiau algebra (DKP algebra), introduced by R.J. Duffin, Nicholas Kemmer and G. Petiau, is the algebra which is generated by the Duffin–Kemmer–Petiau matrices. These matrices form part of the Duffin–Kemmer–Petiau equation that provides a relativistic description of spin-0 and spin-1 particles.

The DKP algebra is also referred to as the meson algebra.

The Duffin–Kemmer–Petiau matrices have the defining relation

where ${\displaystyle \eta ^{ab}}$ stand for a constant diagonal matrix. The Duffin–Kemmer–Petiau matrices ${\displaystyle \beta }$ for which ${\displaystyle \eta ^{ab}}$ consists in diagonal elements (+1,-1,…,-1) form part of the Duffin–Kemmer–Petiau equation. Five-dimensional DKP matrices can be represented as:

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