nLab antiparticle



Fields and quanta

fields and particles in particle physics

and in the standard model of particle physics:

force field gauge bosons

scalar bosons

matter field fermions (spinors, Dirac fields)

flavors of fundamental fermions in the
standard model of particle physics:
generation of fermions1st generation2nd generation3d generation
quarks (qq)
up-typeup quark (uu)charm quark (cc)top quark (tt)
down-typedown quark (dd)strange quark (ss)bottom quark (bb)
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonslight mesons:
pion (udu d)
ρ-meson (udu d)
ω-meson (udu d)
ϕ-meson (ss¯s \bar s),
kaon, K*-meson (usu s, dsd s)
eta-meson (uu+dd+ssu u + d d + s s)

charmed heavy mesons:
D-meson (uc u c, dcd c, scs c)
J/ψ-meson (cc¯c \bar c)
bottom heavy mesons:
B-meson (qbq b)
ϒ-meson (bb¯b \bar b)
proton (uud)(u u d)
neutron (udd)(u d d)

(also: antiparticles)

effective particles

hadrons (bound states of the above quarks)


in grand unified theory

minimally extended supersymmetric standard model




dark matter candidates


auxiliary fields



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.


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 gGg\in G is a group element and χG^\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.


A discussion of traditional and of formalized discussions of antimatter, with an eye towards AQFT, is in


the topic appears around remark 8.79.

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, DOI: 10.

Last revised on July 18, 2023 at 16:45:51. See the history of this page for a list of all contributions to it.