Quantum vacuum state

The lowest-energy state of a quantum field. It contains no particles, yet retains quantum fluctuations and field correlations.

Quantum harmonic oscillator: A quantum system with a restoring force proportional to displacement, whose ground state has nonzero energy. Each independent field mode behaves like an oscillator with a fluctuating ground state.
Quantum field theory: A framework describing particles and their interactions through quantum fields. The vacuum state is defined separately for each quantum field in this framework.
Classical vacuum: A classical field configuration with no matter and typically vanishing field values. Unlike this classical idealization, a quantum vacuum retains fluctuations.
Hawking radiation: Thermal radiation predicted to emerge from black holes because quantum fields propagate in curved spacetime. Black-hole horizons make the choice of vacuum crucial to predicting outgoing particles.
Vacuum energy: The energy density associated with a quantum field's lowest-energy state. Its gravitational significance raises the discrepancy between quantum estimates and cosmological observations.
Zero-point energy: The energy a quantum system retains in its lowest-energy state. Field modes contribute ground-state energy even when no particles are present.
Quantum field: A physical quantity defined throughout spacetime and governed by quantum laws. Its excitations are particles, while its lowest-energy state is the vacuum.
Minkowski vacuum: The Poincaré-invariant vacuum state of quantum fields in flat spacetime. It is the standard vacuum for inertial observers in special-relativistic spacetime.
Particle creation in an expanding universe: The production of field excitations when spacetime expansion changes the definition of positive-frequency modes. Cosmic expansion can make an initial vacuum appear populated with particles.
Cosmological constant problem: The mismatch between naive quantum estimates of vacuum energy and the small observed cosmological constant. It is the sharpest unresolved challenge involving vacuum energy and gravity.

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