Vacuum  

In Classical Physics
* Status: 1998, Best one obtained on Earth has 0.8 cm mean interatom separation (n = 2 atoms/cm3, 5 × 10–17 torr); In interstellar space 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].

In Quantum Mechanics
* 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) [history]; Yam SA(97)dec; Mehra & Rechenberg FP(99) [history].

In Quantum Field Theory > s.a. mass; phase transition; QCD; quantum field theory.
* 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.
@ General references: Milton ht/04-in [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]; Ansoldi a0709-in [semiclassical, and vacuum decay]; Summers a0802-in [overview].
@ Vacuum polarization: Satz et al PRD(05) [around spherical stars].
@ 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. quantum field theory effects in curved spacetime and different backgrounds, theta vacua.

Vacuum Energy > s.a. Conformal Field Theory; Lamb Shift; symmetry breaking [vacuum decay].
* And the cosmological constant: It has often been suggested that the origin of the cosmological constant may be the vacuum energy of quantum fields; In that case, it is susceptible to Casimir-like fluctuations induced by gravitational sources; Another suggestion is that the vacuum energy itself does not gravitate, and the cosmological constant arises from fluctuations; > s.a. cosmological constant.
@ General references: Puthoff PRA(89), comment Wesson PRA(91), reply Puthoff PRA(91), comment Santos PRA(91), reply Puthoff PRA(91) [electromagnetic, origin]; Roberts ht/00 [rev]; Turner in(96)ap/97 [in cosmology]; Fulling JPA(03)qp [and heat kernel coefficients]; Volovik IJMPD(06)gq [myths]; Bruhn PS(06) [energy cannot be extracted]; Holdom NJP(08) [in massless QCD].
@ Non-gravitating: Datta CQG(95); Padmanabhan IJMPD(06)gq.
@ And the cosmological constant: Sahni MPLA(99); Razmi & Abbassi qp/99 [different approach]; Rugh & Zinkernagel SHPMP(02)ht/00 [conceptual]; Genet et al qp/02-in [rev]; Ford gq/02-in; Volovik AdP(05)gq/04; Marsh a0711 [need to redefine vacuum].

Vacuum Fluctuations > s.a. casimir effect; decoherence; fluctuations; higher-order gravity; quantum gravity phenomenology; stochastic quantum mechanics.
* Zero-point fluctuations: Those corresponding to the residual energy a field has in the vacuum state.
* Applications: Used to explain stability of atoms, Zitterbewegung, Casimir effect, Vilenkin's universe from nothing, black hole radiation; Have been proposed as explanation for cosmological constant.
@ General references: Reynaud et al CRAS(01)qp; Santos qp/02 [reality]; Brustein & Oaknin PRD(03)ht/02 [pseudoclassical description].
@ And photon detectors: Santos qp/02; Marshall & Santos a0707 [classical model].
@ And atoms: NS(87)jul, NS(90)jul28 [stability]; Stenger et al PRL(99) [in Bose-Einstein condensates].
@ And decoherence: Santos PLA(94); Ellis et al qp/97-in; Kim et al PRL(06) [dissipation, proposed experiment]; > s.a. particle effects [creation], quantum field theory effects in curved spacetime [quantum radiation].
@ And gravity, inertia: Stefanski & Bedford AJP(94); Jaekel & Reynaud RPP(97)qp; Modanese FPL(03)ht/00; Rueda et al gq/01; Caldwell ap/02 [and Casimir effect]; Jaekel et al NAR(02); Padmanabhan IJMPD(06); Beck & Mackey PhyA(07) [and dark energy]; > s.a. inertia.
@ Focusing: Ford & Svaiter PRA(00)qp, PRA(02)qp [with mirrors].
@ Related topics: NS(89)dec2 [self-regenerating theory]; Kazakov JPA(06) [from quantum matter in external E field]; > s.a. correlations.

Other Concepts / Effects > s.a. cosmological constant; entanglement; photon; quantum field theory in curved spacetime; radiation [pressure].
$ Vacuum persistence amplitude: The quantity

Z[J]:= 0+ | 0–J = D exp{ i (S[] + J[])} .

* Sparking of the vacuum: A non-perturbative QED effect in atomic physics; An atom with binding energy for the lowest-lying electron orbit greater that 2mec2, in a supercritical electrostatic field, would find it convenient to create an e+e– pair and emit the positron; Such superheavy nuclei (Z > 173) do not exist, but the effect should show up as a Z-dependent and not too narrow peak in the positron spectrum in heavy ion collisions.
@ Uniqueness issues: Sachs PRL(94); Schützhold et al ht/00 [4]; > s.a. superselection rules.
@ Related topics: Weigert PLA(96) [squeezing and Casimir]; Pettorino & Vilkovisky AP(01) [vmax of sources]; Scandurra ht/01 [thermodynamics]; Kunhardt mp/01-PhD [massless particles and "infravacua"]; Feigel PRL(04) [motion from vacuum]; > s.a. brownian motion.

General References
@ I: Greiner & Hamilton AS(80); Von Baeyer ThSc(87)mar; Boyer SA(85)aug; Barrow 00, 07.
@ Books: Grant 81 [historical]; Genz 99; Saunders & Brown ed-91 [philosophical].
@ Physical: Aitchison CP(85); Sciama in(91); Zichichi ed-96; Brandt qp/03 [heuristics].
@ QED: Marshall PRS(63); Milonni PS(88), 94; Hofmann et al OE(98)qp/97 [fluctuations]; Greiner & Schramm AJP(08)RL.
@ QED, stability: Azam ht/01 [and Landau pole]; Solomon Ap(06)ht/04; Azam a0806.
@ Other theories: DeGrand et al NPB(97) [SU(2)]; Paniak et al NPB(97) [2D gauge theory].

Vacuum in Quantum Gravity > s.a. spacetime foam.
* Choice: The natural candidate for ground state of the equation Gab= 8G Tab, flat spacetime gab = ab, is not stable [may be false!]; The ground state for quantum gravity may not be a Gaussian centered around Minkowski.
@ References: Horowitz in(81); Penrose in(91); Padmanabhan & Choudhury MPLA(00)gq.

Main page – Abbreviations – Journals – Comments – Other sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified 12 jul 2008