nLab antiparticle

Idea

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 $G$ such a model can be created, and quasiparticles can be explicitly described. They correspond to pairs $(g,\chi)$ where $g\in G$ is a group element and $\chi\in \widehat{G}$ is a character. The antiparticle is $(g^{-1},\chi^{-1})$, 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.

Related concepts

• dilepton

• CPT theorem

• anti-D-brane

• topological quantum field theory

• rigid category

References

General exposition:

• Beatriz Gato-Rivera: Antimatter [arXiv:2412.12128]

See also:

• Wikipedia: Antimatter

On traditional and formalized discussions of antimatter, with an eye towards AQFT:

• David Baker, Hans Halvorson, Antimatter (pdf)

• Hans Halvorson, around Remark 8.79 in Algebraic quantum field theory [pdf]

See also:

• R. Ascoli, G. Teppati und S. Termini: Some remarks about particle-antiparticle superselection rules, Lettere Al Nuovo Cimento (1969 - 1970) Volume 1, Number 4 (1969), 223-227 [pdf, doi:10.1007/BF02752486]