In quantum field theory, the quantum vacuum state (also called the quantum vacuum or vacuum state) is the quantum state with the lowest possible energy. Generally, it contains no physical particles. However, the quantum vacuum is not a simple empty space, but instead contains fleeting electromagnetic waves and particles that pop into and out of the quantum field. The QED vacuum of quantum electrodynamics (or QED) was the first vacuum of quantum field theory to be developed. QED originated in the 1930s, and in the late 1940s and early 1950s, it was reformulated by Feynman, Tomonaga, and Schwinger, who jointly received the Nobel prize for this work in 1965. Today, the electromagnetic interactions and the weak interactions are unified (at very high energies only) in the theory of the electroweak interaction. The Standard Model is a generalization of the QED work to include all the known elementary particles and their interactions (except gravity). Quantum chromodynamics (or QCD) is the portion of the Standard Model that deals with strong interactions, and the QCD vacuum is the vacuum of quantum chromodynamics. It is the object of study in the Large Hadron Collider and the Relativistic Heavy Ion Collider, and is related to the so-called vacuum structure of strong interactions.
Non-zero expectation value
If the quantum 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, or more accurately, the ground state of a measurement problem. In this case, the vacuum expectation value 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 obtain non-vanishing vacuum expectation values by spontaneous symmetry breaking. In the Standard Model, the Higgs field acquires a non-zero expectation value when the electroweak symmetry is broken, and this explains part of the masses of other particles.
Energy
The vacuum state is associated with a zero-point energy, and this zero-point energy (equivalent to the lowest possible energy state) has measurable effects. It may be detected as the Casimir effect in the laboratory. In physical cosmology, the energy of the cosmological vacuum appears as the cosmological constant. The energy of a cubic centimeter of empty space has been calculated figuratively to be one trillionth of an erg (or 0.6 eV). An outstanding requirement imposed on a potential Theory of Everything is that the energy of the quantum vacuum state must explain the physically observed cosmological constant.
Symmetry For a relativistic field theory, the vacuum is Poincaré invariant, which follows from Wightman axioms but can also be proved directly without these axioms. Poincaré invariance implies that only scalar combinations of field operators have non-vanishing vacuum expectation values. The vacuum 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.
Non-linear permittivity
Quantum corrections to Maxwell's equations are expected to result in a tiny nonlinear electric polarization term in the vacuum, resulting in a field-dependent electrical permittivity ε deviating from the nominal value ε0 of vacuum permittivity. These theoretical developments are described, for example, in Dittrich and Gies. The theory of quantum electrodynamics predicts that the QED vacuum should exhibit a slight nonlinearity so that in the presence of a very strong electric field, the permittivity is increased by a tiny amount with respect to ε0. Subject to ongoing experimental efforts is the possibility that a strong electric field would modify the effective permeability of free space, becoming anisotropic with a value slightly below μ0 in the direction of the electric field and slightly exceeding μ0 in the perpendicular direction. The quantum vacuum exposed to an electric field exhibits birefringence for an electromagnetic wave traveling in a direction other than the electric field. The effect is similar to the Kerr effect but without matter being present. This tiny nonlinearity can be interpreted in terms of virtual pair production. A characteristic electric field strength for which the nonlinearities become sizable is predicted to be enormous, about 1.32 × 10 18 {\displaystyle 1.32\times 10^{18}} V/m, known as the Schwinger limit; the equivalent Kerr constant has been estimated, being about 1020 times smaller than the Kerr constant of water. Explanations for dichroism from particle physics, outside quantum electrodynamics, also have been proposed. Experimentally measuring such an effect is challenging, and has not yet been successful.
Virtual particles
The presence of virtual particles can be rigorously based upon the non-commutation of the quantized electromagnetic fields. Non-commutation means that although the average values of the fields vanish in a quantum vacuum, their variances do not. The term "vacuum fluctuations" refers to the variance of the field strength in the minimal energy state, and is described picturesquely as evidence of "virtual particles". It is sometimes attempted to provide an intuitive picture of virtual particles, or variances, based upon the Heisenberg energy-time uncertainty principle:
Δ E Δ t ≥ ℏ 2 , {\displaystyle \Delta E\Delta t\geq {\frac {\hbar }{2}}\,,}
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