nLab false vacuum

1. Idea

A classical field theory with action functional having the standard kinetic action and non-derivative interactions has stable, time-independent solutions to its equations of motion where all fields are constant on a value that is a local minimum of the interaction term potential energy (if any).

In the corresponding quantum field theory, however, a state that is initially concentrated this way on a local minimum which is not also a global minimum is not time-independent, but will exhibit quantum tunneling behaviour by which the fields “tunnel” through the local potential barrier into the global minimum. Therefore one speaks of a false vacuum in this case.

2. Examples

• Higgs field – Mass and Vacuum (in-)stability

3. Related concepts

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

4. References

The classical articles are

• Sidney Coleman, Fate of the false vacuum: Semiclassical theory , Phys. Rev. D 15, 2929–2936 (1977) (doi:10.1103/PhysRevD.15.2929)

• Sidney Coleman, Frank De Luccia, Gravitational effects on and of vacuum decay , Phys. Rev. D 21, 3305–3315 (1980) (doi:10.1103/PhysRevD.21.3305)

More recent development (in view of Higgs metastability):

• Anders Andreassen, David Farhi, William Frost, Matthew D. Schwartz, Precision decay rate calculations in quantum field theory, Phys. Rev. D 95, 085011 (2017) (arXiv:1604.06090)