Vacuum expectation value ( $⟨ ϕ ⟩$ )

A vacuum expectation value is the expectation of a field or operator in the vacuum state. A nonzero value that is not invariant under the full symmetry group can select a point of the vacuum manifold and spontaneously break the symmetry.

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The vacuum expectation value (VEV) is a concept in quantum field theory (QFT) that refers to the average value of a field (or an operator) in the vacuum state. The vacuum state is the lowest energy state of a quantum system, often viewed as the ground state that has no particles present.

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