If particles species are identified simple objects of a DHR category, then the elements of the corresponding dual object are called antiparticles.

Similarly, in the (2+1)-TQFT setting isomorphism classes of quasiparticles will correspond to simple objects of a modular tensor category. The anti-quasiparticle of a quasiparticle is its dual, under the rigidity structure of your category.

Examples

In the standard model of particle physics, every particle has an antiparticle. For example, the antiparticle of the electron is the positron.

In the realm of (2+1)-TQFTs, the most simple example is the quantum double anyon model applied to an abelian group. For every finite abelian group GG such a model can be created, and quasiparticles can be explicitly described. They correspond to pairs (g,χ)(g,\chi) where g∈Gg\in G is a group element and χ∈G^\chi\in \widehat{G} is a character. The antiparticle is (g −1,χ −1)(g^{-1},\chi^{-1}), where both the inverses are taken with respect to the group operation.

Just like inverses play a key role in the theory of finite groups, antiparticles play a key role in the theory of (2+1)-TQFTs and modular tensor categories.

References

General exposition:

Beatriz Gato-Rivera: Antimatter [arXiv:2412.12128]