nLab interacting vacuum

Idea

A vacuum state for an interacting field theory is sometimes called, for emphasis, an interacting vacuum.

In perturbative quantum field theory one starts with a free field theory and a vacuum state (or Hadamard vacuum state) on that, the “free vacuum”; and then finds, perturbatively, the interacting field algebra of observables. The free vacuum is typically still a state on the interacting field algebra of observables, but it is in general no longer a vacuum state with respect to the interacting field algebra. To highlight the difference to an actual vacuum state for the interacting field algebra, one speaks of the interacting vacuum (e.g. Rafelski 90).

Issues related to the adiabatic limit and infrared divergences in perturbative QFT are argued to be related to the need to pass to the correct interacting vacuum (Duch 17, p. 113-114).

This is understood to some extent in quantum electrodynamics but remains a major open problem in quantum chromodynamics (below).

Examples

In QCD

There are arguments that the phenomenon of confinement in QCD will be explained by finding the properly interacting vacuum of the perturbative theory (Rafelski 90, around pages 12-16). Possibly this is a “theta-vacuum” reflecting QCD instanton contributions (Schäfer-Shuryak 98, section III D).

Related concepts

• non-perturbative effect

quantum probability theory – observables and states

• states

  • classical state

  • quantum state

    • space of states (in geometric quantization)

    • state on a star-algebra, quasi-state

    • qbit, Bell state

      dimer, tensor network state

    • quantum state preparation

    • probability amplitude, quantum fluctuation

    • pure state

      • wave function

      • bra-ket

      • Bell state

    • quantum superposition, quantum interference

    • quantum entanglement

    • quantum measurement

      wave function collapse

      Born rule

      deferred measurement principle

      quantum reader monad

      measurement problem

    • superselection sector

    • mixed state, density matrix

      entanglement entropy

      holographic entanglement entropy

    • coherent quantum state

  • ground state, excited state

  • quasi-free state

  • Fock space, second quantization

  • vacuum, vacuum state

    • Hadamard state

    • vacuum diagram

    • vacuum expectation value, vacuum amplitude, vacuum fluctuation

    • vacuum energy

    • vacuum polarization

    • interacting vacuum

    • thermal vacuum, KMS state

    • vacuum stability

      • false vacuum, tachyon, Coleman-De Luccia instanton

    • theta vacuum

    • perturbative string theory vacuum

      • non-geometric string theory vacuum

      • landscape of string theory vacua

  • entangled state

  • tensor network state

    • matrix product state

    • tree tensor network state

• observables

  • quantum observable, beable

  • algebra of observables, star-algebra

  • Bohr topos

  • quantum operator (in geometric quantization)

  • quantum operation, quantum effect, effect algebra

  • in quantum field theory

    • local observable

    • polynomial observable

      • linear observable

        • field observable

    • regular observable

    • microcausal observable

    • normal-ordered product, time-ordered products, retarded product

    • Wick algebra

    • scattering amplitude

    • interacting field algebra of observables, Bogoliubov's formula

• GNS construction

• theorems

  • order-theoretic structure in quantum mechanics

    • Gleason's theorem

    • Alfsen-Shultz theorem

    • Harding-Döring-Hamhalter theorem

    • Kochen-Specker theorem

    • Nuiten's lemma

  • Wigner's theorem

  • no-cloning theorem

  • Bell's theorem

References

• Johann Rafelski, Vacuum structure – An Essay, in pages 1-29 of H. Fried, Berndt Müller (eds.) Vacuum Structure in Intense Fields, Plenum Press 1990 (GBooks)

• Thomas Schaefer, Edward Shuryak, Instantons in QCD, Rev. Mod. Phys.70:323-426,1998 (arXiv:hep-ph/9610451)

• Paweł Duch, Massless fields and adiabatic limit in quantum field theory (arXiv:1709.09907)