- Vacuum state
In

quantum field theory , the**vacuum state**(also called the**vacuum**) is thequantum state with the lowest possibleenergy . Generally, it contains no physical particles. The term "zero-point field " is sometimes used as a synonym for the vacuum state of an individual quantized field.According to present-day understanding of what is called the vacuum state or the quantum vacuum, it is "by no means a simple empty space"cite book

author=Astrid Lambrecht (Hartmut Figger, Dieter Meschede, Claus Zimmermann Eds.)

title=Observing mechanical dissipation in the quantum vacuum: an experimental challenge; in**Laser physics at the limits**

page=p. 197

publisher= Springer

location=Berlin/New York

year=2002

isbn=3540424180

url=http://books.google.com/books?id=0DUjDAPwcqoC&pg=PA197&dq=%22vacuum+state%22&lr=&as_brr=0&sig=-gfWcR7RdymYL3W-M2VxVQPFm10#PPA197,M1] , and again: "it is a mistake to think of any physical vacuum as some absolutely empty void."cite book

author=Christopher Ray

title=Time, space and philosophy

page=Chapter 10, p. 205

publisher= Routledge

location=London/New York

year=1991

isbn=0415032210

url=http://books.google.com/books?id=1F7xWULz0P0C&pg=RA1-PA205&dq=%22vacuum+state%22&lr=&as_brr=0&sig=3jx_vuLEBKXfGNEY4CfUIDTPVSI] According to quantum mechanics, the vacuum state is not truly empty but instead contains fleeting electromagnetic waves and particles that pop into and out of existence. [*[*] [*http://www.aip.org/pnu/1996/split/pnu300-3.htm AIP Physics News Update,1996*]*[*] cite book*http://focus.aps.org/story/v2/st28 Physical Review Focus Dec. 1998*]

author=Walter Dittrich & Gies H

title=Probing the quantum vacuum: perturbative effective action approach

publisher= Springer

location=Berlin

year=2000

isbn=3540674284

url=http://books.google.com/books?id=DyhyFSL7bNUC&pg=PP1&dq=intitle:Probing+intitle:the+intitle:Quantum+intitle:Vacuum&lr=&as_brr=0&sig=VSfMMLJnmYyWplC2L5i9oVSjurg#PPA1,M1]The

QCD vacuum ofquantum chromodynamics is the object of study in the relativistic heavy ion collider and thelarge hadron collider , and is related to the so-called "vacuum structure ofstrong interactions ".cite book |title=Hadrons and Quark-Gluon Plasma |author=Jean Letessier, Johann Rafelski |page=pp. 37 "ff" |url=http://books.google.com/books?id=vSnFPyQaSTsC&pg=PR11&vq=Qgp+state&dq=weinberg+%22symmetry+%22&lr=&as_brr=0&source=gbs_search_s&sig=ACfU3U1Xur2r-R1LuGFmURrLEYXMFK9Syw#PPA38,M1 |isbn=0521385369 |year=2002 |publisher=Cambridge University Press]**Non-vanishing vacuum state**If the quantum field theory can be accurately described through

perturbation theory , then the properties of the vacuum are analogous to the properties of theground state of a quantum mechanicalharmonic oscillator (or more accurately, theground state of a QM problem). In this case thevacuum expectation value (VEV) of any field operator vanishes. For quantum field theories in whichperturbation theory breaks down at low energies (for example,Quantum chromodynamics or theBCS theory ofsuperconductivity ) field operators may have non-vanishingvacuum expectation value s called condensates. In theStandard Model , the non-zero vacuum expectation value of theHiggs field , arising fromspontaneous symmetry breaking , is the mechanism by which the other fields in the theory acquire mass.**The energy of the vacuum state**In many situations, the vacuum state can be defined to have zero energy, although the actual situation is considerably more subtle. The vacuum state is associated with a

zero-point energy , and this zero-point energy has measurable effects. In the laboratory, it may be detected as theCasimir effect . Inphysical cosmology , the energy of the vacuum state appears as thecosmological constant . An outstanding requirement imposed on a potentialTheory of Everything is that the energy of the vacuum state must explain the physically observed cosmological constant.**The symmetry of the vacuum state**For a relativistic field theory, the vacuum is Poincaré invariant. Poincaré invariance implies that only

scalar combinations of field operators have non-vanishing VEV's. The VEV may break some of theinternal symmetries of theLagrangian of the field theory. In this case the vacuum has less symmetry than the theory allows, and one says that "spontaneous symmetry breaking " has occurred. SeeHiggs mechanism ,standard model and Woit.cite book

author=Peter Woit

title=Not even wrong: the failure of string theory and the search for unity in physical law

publisher= Basic Books

location=New York

year=2006

isbn=0465092756

url=http://books.google.com/books?id=pcJA3i0xKAUC&pg=PA93&dq=%22Higgs+field%22&lr=&as_brr=0&sig=I168cJKoVyLqOd7z9pdeR0mC_A0#PPA71,M1]**Electrical permittivity of vacuum state**In principle, it is possible for the experimental electrical permittivity ε of the vacuum state to deviate from the defined scalar value ε

_{0}of theelectric constant due to quantum corrections to Maxwell's equations. These theoretical developments are described, for example, in Dittrich and Gies.cite book

author=Walter Dittrich & Gies H

title=Probing the quantum vacuum: perturbative effective action approach

publisher= Springer

location=Berlin

page=p. 13, for example

year=2000

isbn=3540674284

url=http://books.google.com/books?id=DyhyFSL7bNUC&pg=PP1&dq=intitle:Probing+intitle:the+intitle:Quantum+intitle:Vacuum&lr=&as_brr=0&sig=VSfMMLJnmYyWplC2L5i9oVSjurg#PPA13,M1] In particular, the theory ofquantum electrodynamics predicts that vacuum should exhibit nonlinear effects that will make it behave like abirefringent material with ε slightly greater than ε_{0}for extremely strong electric fields. [*Klein, James J. and B. P. Nigam, [*] Mourou, G. A., T. Tajima, and S. V. Bulanov, [*http://prola.aps.org/abstract/PR/v135/i5B/pB1279_1 "Birefringence of the vacuum"*] , "Physical Review" vol.**135**, p. B1279-B1280 (1964).*http://acc-physics.kek.jp/sokensympo/frontier_accelerator/FACW1-PROC/FACW1-23.1.pdf "Optics in the relativistic regime"; § XI "Nonlinear QED"*] , "Reviews of Modern Physics" vol.**78**(no. 2), 309-371 (2006).] Explanations fordichroism from particle physics, outside quantum electrodynamics, also have been proposed. [*[*] Active attempts to measure such effects have been unsuccessful so far. [*http://arxiv.org/abs/hep-ph/0607118 Gies, H "et al.": "Polarized light propagating in a magnetic field as a probe for millicharged fermions"*] Phys. Rev. Letts.**97**(2006) 140402*[*]*http://arxiv.org/abs/0704.0748 CC Davis "et al. " "Experimental challenges involved in searches for ... nonlinear QED effects by sensitive optical techniques"*]**Notations**The vacuum state is written as $|0\; angle$ or $|\; angle$. The VEV of a field φ, which should be written as $langle0|phi|0\; angle$, is usually condensed to $langlephi\; angle$.

**Virtual particles**The

uncertainty principle in the form $Delta\; EDelta\; tgehbar$ implies that in the vacuum one or more particles with energy ΔE above the vacuum may be created for a short time Δt. These "virtual particles " are included in the definition of the vacuum.**ee also***

Vacuum energy

*Virtual particle

*Pair production

*Vacuum polarization

*The quantum-mechanical vacuum

*QCD vacuum

*Squeezed coherent state

*Casimir effect

*Van der Waals force

*Free space **References and notes****Further reading*** M.E. Peskin and D.V. Schroeder, "An introduction to Quantum Field Theory".

* H. Genz, " Nothingness: The Science of Empty Space"

*Wikimedia Foundation.
2010.*