In Classical Physics
* History: In antiquity, Plato and Aristotle thought that a vacuum could not exist; In medieval Europe to discuss a vacuum became heretical and dangerous ("Nature abhors a vacuum"); 1550, The word "vacuum" is first used in English, by Thomas Cranmer (Archbishop of Canterbury) in the Book of Common Prayer; 1644, Evangelista Torricelli produced the first vacuum in the laboratory and brought the concept into experimental physics, as part of his solution to a mystery that frustrated Tuscan well diggers; When they tried to raise water more than about 10 m, the water would separate from the well plunger and rise no further; Galileo considered the problem, but died with it unresolved; Torricelli did not make his results public at first, but showed the experiment to Marin Mersenne, who then told Pascal and made the news public in France.
* Status: 1998, The best one obtained on Earth has a 0.8-cm mean interatom separation (n = 2 atoms/cm3, 5 × 10−17 torr); In interstellar space, the separation is 1 cm; In the galactic halo, 10 cm; In intergalactic space, 10 m [@ NS(98)apr10].
@ References: Herbert pw(07)jul [challenges of vacuum technology]; Williams APS(12)oct [Torricelli].

In Quantum Mechanics > s.a. fluctuations.
* Zero-point energy: Introduced by Max Planck in the spring of 1911, as a heuristic principle in the early struggles to establish the concept of the energy quantum.
* Zero-point fluctuations: Those corresponding to the residual energy an oscillator has in the ground state.
@ Zero-point energy: Boyer AP(70) [and long-range forces]; Puthoff PRD(87) [and H ground level]; Milonni & Shih AJP(91)aug [history]; Yam SA(97)dec; Mehra & Rechenberg FP(99) [history]; de la Peña et al AJP(08)oct [harmonic oscillator, and Planck's law]; Bellazzini et al JHEP(16)-a1502 [cosmological and astrophysical probes].
@ Zero-point fluctuations: Morello et al PRL(14)-a1311 [single-molecule magnet, observation].

In Quantum Field Theory > s.a. mass; vacuum phenomenology [fluctuations, entanglement, different types of theories].
* Vacuum state: A state which gives zero when acted upon by the annihilation operators associated with all modes of a complete set defined using a timelike (Killing) vector field; Also, a pure, quasi-free state.
* Properties: In Minkowski quantum field theories it has zero conserved quantities, and is Poincaré-invariant.
* Vacuum-to-vacuum transition amplitude: The amplitude Z[J] in the presence of an external source, usually calculated using a path intergal; It is the generator for the n-point Green's functions.
@ General references: Milton IJMPA(05)ht/04-conf [hadronic physics]; Ford & Roman PRD(05)gq [stress-energy fluctuations and correlations]; Fulling PLB(05)mp [regularized]; Rizzo & Rikken PS(05) [magneto-electro-optical properties]; Solomon PS(06)qp [in Dirac hole theory]; Summers a0802-conf [overview]; Volovik a1004-ch [phenomenology, superfluid], LNP-a1111 [topology]; Bednorz EPJC(13)-a1209 [relativistic invariance]; Paraoanu ch(15)-a1402; Kothawala a1612 [vacuum energy density, and spacetime curvature].
@ In Maxwell theory: Prykarpatsky & Bogolubov a0807; Karbstein a1611-ln.
@ In Yang-Mills theory: Olejník JPCS(15)-a1503; Aitken et al JHEP(18)-a1804 [as a function of θ].
@ Uniqueness issues: Sachs PRL(94); Schützhold et al ht/00 [λφ4]; Dybalski CMP(08); > s.a. superselection rules.
@ Vacuum-to-vacuum amplitude: Solomon a1406 [from the time evolution operator].
@ Vacuum polarization: Satz et al PRD(05) [around spherical stars]; Fujita et al a0901 [new renormalization scheme]; Jentschura PRA(15)-a1501 [gravitational corrections]; Izadi Rad a1701 [experiment with superconducting junctions]; Wernersson & Zahn a2010 [effect of boundary conditions].
@ Instability, false vacuum decay: Ansoldi PoS-a0709 [semiclassical]; Cardella et al JHEP(08)-a0807 [no resonant decay in scalar gauge theories]; Álvarez & Vidal JCAP(10)-a1004 [instability with an external gravitational field, de Sitter spacetime case]; Garriga et al JCAP(11) [Minkowski vacua can be metastable]; Gregory et al JHEP(14)-a1401 [black holes as bubble nucleation sites]; Rajantie & Stopyra PRD(17)-a1606 [in the Standard Model, with gravity]; Urbanowski TMP(17)-a1609 [survival probability]; Endo et al JHEP(17)-a1704 [in gauge theories]; Braden et al a1806 [new semiclassical picture]; Bachlechner a1809 [in general relativity]; Wang PRD(19)-a1909 [semiclassical]; Michel a1912 [real-time approach]; > s.a. instantons; symmetry breaking.
@ Space of vacuum states: Niedermaier & Seiler CMP(07)mp/06 [with non-amenable symmetries].
@ Inequivalent vacua: Winters-Hilt et al PRD(99) [flat space]; > s.a. qft in curved spacetime, effects and different backgrounds; theta vacua.
@ Vacuum amplification / dominance: Oikonomou G&C(13)-a1308 [scalar field and electric field]; > s.a. semiclassical gravity.
> Related topics: see Sorkin-Johnston Vacuum; types of measurements [non-demolition vacuum measurement].

General References > s.a. quantum field theory.
@ I: Greiner & Hamilton AS(80)mar; Von Baeyer ThSc(87)mar; Boyer SA(85)aug; Barrow 00, 07; Boi 11 [r CP(12)]; Weatherall 16 [r PT(17)].
@ Books: Grant 81 [historical]; Genz 99; Saunders & Brown ed-91 [philosophical]; Close 09.
@ Physical: Aitchison CP(85); Sciama in(91); Zichichi ed-96; Brandt qp/03 [heuristics]; Consoli et al PhyA(14) [the vacuum as a turbulent fluid].

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