Vacuum state
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In quantum field theory, the vacuum state (also called the vacuum) is the quantum state with the lowest possible energy. As a result, it contains no physical particles. Conventionally it has zero energy (see however cosmological constant).
For a relativistic field theory, the vacuum is Poincaré invariant. If the field theory can be accurately described through perturbation theory, then the properties of the vacuum are analogous to the properties of the ground state of a quantum mechanical harmonic oscillator. In this case the vacuum expectation value (VEV) of any field operator vanishes. For quantum field theories in which perturbation theory breaks down at low energies (for example, Quantum chromodynamics or the BCS theory of superconductivity) field operators may have non-vanishing vacuum expectation values called condensates.
Poincare invariance implies that only scalar combinations of field operators have non-vanishing VEVs. The VEV may break some of the internal symmetries of the Lagrangian of the field theory. In this case the vacuum has less symmetry than the theory allows, and one says that spontaneous symmetry breaking has occurred.
The vacuum state is written as <math>|0\rangle<math> or <math>|\rangle<math>. The VEV of a field φ, which should be written as <math>\langle0|\phi|0\rangle<math>, is usually condensed to <math>\langle\phi\rangle<math>.
The uncertainty principle in the form <math>\Delta E\Delta t\ge\hbar<math> implies that in the vacuum one or more particles with energy ΔE above the vacuum may be created for a short time Δt. These virtual particles are included in the definition of the vacuum.
See also
References
- An introduction to Quantum Field Theory, by M.E. Peskin and D.V. Schroeder (http://www.amazon.com/exec/obidos/ASIN/0201503972/qid=1117615919/sr=2-1/ref=pd_bbs_b_2_1/102-3287261-6119321)