= Vacuum energy
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Vacuum energy is the <energy> assigned to a theory's <vacuum state>. In a free bosonic field description it includes the sum of oscillator <zero-point energies>, formally $\tfrac12\sum_{\mathbf k}\hbar\omega_{\mathbf k}$. The continuum limit of that expression is generally divergent and requires a prescription, rather than direct identification with a finite measured energy density.
Adding a constant to a nongravitational <Hamiltonian> changes an overall evolution phase but not transition <probabilities>. Energy differences between boundary configurations can nevertheless have physical effects, as in the <Casimir effect>. When gravity is included, a vacuum energy density contributes to the gravitational source and is related to the <cosmological constant>. <Normal ordering> removes a reference-theory constant by convention; it does not solve every interacting or gravitational vacuum-energy problem.
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