nLab bound state

Examples

The hierarchy of bound states in quantum chromodynamics:

• if quarks themselves were bound states (which they are not according to the standard model of particle physics) then one would call them bound states of preons

• hadrons are bound states of quarks

  (and of gluons, while glueballs are bound states purely of gluons)

  (at temperatures that these bound states decay one speaks of a quark gluon plasma)

  • mesons are bound states specifically of two quarks

    • pions, rho-mesons and omega-mesons are bound states of an up quark with a down quark

    • kaons are bound states of a strange quark with either an up quark or a down quark

    • B-mesons are bound states of a bottom quark with either an up quark or a down quark or a strange quark or a charm quark

  • baryons are bound states specifically of three quarks, or rather of one quark and a diquark

    • nuclei are bound states of three among the up quarks and the down quarks

      • protons are bound states of 2 up quarks and 1 down quark

      • neutrons are bound states of 1 up quarks and 2 down quark

• atomic nuclei are bound states of of nuclei (protons and neutrons)

• atoms are bound states of atomic nuclei and electrons

  (at temperature high enough that these bound states decay, one speaks of a plasma)

  • in particular hydrogen atoms are bound states of a proton and an electron

• molecules are bound states of atoms

Here the last two steps go beyond QCD as they also involve electrons from quantum electrodynamics.

There are also bound states purely in QED:

• positronium is a bound state of an electron and a positron

Hypothetically:

• a composite Higgs boson would be a bound state of a strongly interacting sector beyond the current standard model of particle physics

brane intersections/bound states/wrapped branes/polarized branes

• D-branes and anti D-branes form bound states by tachyon condensation, thought to imply the classification of D-brane charge by K-theory

• intersecting D-branes/fuzzy funnels:

  • Dp-D(p+2)-brane bound state and Yang-Mills monopoles

    • D0-D2 brane bound state

    • D1-D3 brane bound state

    • D2-D4 brane bound state

    • D3-D5 brane bound state

    • D4-D6 brane bound state

    • D6-D8-brane bound state

  • Dp-D(p+4)-brane bound state and Yang-Mills instantons

    • D0-D4 brane bound state

    • D1-D5 brane bound state

    • D2-D6 brane bound state

    • D3-D7 brane bound state

    • D4-D8 brane bound state

    • D5-D9 brane bound state

      small instanton

• Dp-D(p+6) brane bound state

  • D0-D6 brane bound state

  • D1-D7 brane bound state

  • D2-D8 brane bound state

• NS5-D4-D2 bound states

• Hanany-Witten effect

S-duality$\,$bound states:

• (p,q)-string

• (p,q)5-branes

• string network

• 5-brane web

intersecting$\,$M-branes:

• M5-MO9 brane bound state

• M2-M5 brane bound state

  • M-string, E-string

• membrane triple junction

Related concepts

• binding energy

• quantum state

References

On bound states in QED and QCD:

• Paul Hoyer, Bound states – from QED to QCD, Lectures at “Mini-school on theoretical methods in particle physics” at the Higgs Centre for Theoretical Physics, University of Edinburgh on 30 September to 4 October 2013 (arXiv:1402.5005)

• Changyong Liu, On bound states in Quantum Field Theory (arXiv:1811.06457)

• Paul Hoyer, Journey to the Bound States (arXiv:2101.06721)

See also

• Wikipedia, Bound state