Decoding methods - Revision history

213.49.91.158: /* Syndrome decoding */ which allows what?

2014-08-10T14:48:28Z

Syndrome decoding: which allows what?

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	In [[quantum field theory]], and specifically [[quantum electrodynamics]], '''vacuum polarization''' describes a process in which a background [[electromagnetic field]] produces [[virtual particle\|virtual electron]]–[[positron]] pairs that change the distribution of charges and currents that generated the original electromagnetic field. It is also sometimes referred to as the '''[[self energy]]''' of the [[gauge boson]] ([[photon]]).		29 year old Agricultural Consultant Bob from Three Hills, has many passions including scrapbooking, new launch property singapore and kids. Intends to quit work and take the family to numerous noteworthy heritage listed places on the planet for example Choirokoitia.<br><br>My web page - [http://www.quipux.org.ec/?q=node/32426 The Skywoods developer]

	The effects of vacuum polarization were first observed experimentally prior to 1947 before they were theoretically calculated (by [[Hans Bethe]] on the return train ride from the [[Shelter Island Conference]] to Cornell) after developments in radar equipment for [[World War II]] resulted in higher accuracy for measuring the energy levels of the hydrogen atom (the [[Lamb shift]]) and the [[anomalous magnetic dipole moment]] of the electron (corresponding to the deviation from ~~the [[Dirac equation]] predicted value of 2 of the spectroscopic electron [[g-factor (physics)\|g-factor]] value)~~, ~~measured by [[I.I. Rabi]].~~

	The effects of vacuum polarization have been routinely observed experimentally since then as very well understood background effects. Vacuum polarization referred to below as the one loop contribution occurs with leptons (electron-positron pairs) or quarks, ~~the former (leptons) first observed in 1940s but also recently observed in 1997 using the [[TRISTAN]] particle accelerator in Japan,<ref>{{cite journal~~
	~~\| last=Levine \| first=I. \| coauthors=TOPAZ Collaboration~~
	~~\| title=Measurement of the Electromagnetic Coupling at Large Momentum Transfer~~
	~~\| journal=Physical Review Letters \| year=1997~~
	~~\| volume=78 \| pages=424–427~~
	~~\| doi=10.1103/PhysRevLett.78.424 \| bibcode=1997PhRvL..78..424L~~
	~~\| issue=3}}</ref>~~
	the latter (quarks) along with multiple quark-gluon loop contributions from the early 1970s to mid-1990s using the VEPP-2M particle accelerator at the [[Budker Institute of Nuclear Physics]] in [[Siberia]] in [[Russia]] and ~~many other accelerator laboratories worldwide.<ref>{{cite journal~~
	~~\| last=Brown \| first=Douglas H \| coauthors=Worstell, William A~~
	~~\| title=The Lowest Order Hadronic Contribution to the Muon g − 2 Value with Systematic Error Correlations~~
	~~\| journal=Physical Review D \| year=1996~~
	~~\| volume=54 \| pages=3237–3249~~
	~~\| doi=10.1103/PhysRevD.54.3237~~
	~~\| issue=5\|arxiv = hep-ph/9607319 \|bibcode = 1996PhRvD~~.~~.54.3237B }}</ref>~~

	~~== Explanation ==~~
	~~According~~ to [[quantum field theory]], the vacuum between interacting particles is not simply empty space. Rather, it contains short-lived [[virtual particle\|"virtual" particle–antiparticle pairs]] ([[leptons]] or [[quarks]] and ~~[[gluons]]) which are created out of~~ the vacuum in amounts of energy constrained in time by the energy-time version of the Heisenberg [[uncertainty principle]]. After the constrained time, which is smaller (larger) the larger (smaller) the energy of the fluctuation, they then annihilate each other.

	~~These particle–antiparticle pairs carry various kinds of charges, such as [[color charge]] if they are subject~~ to [[Quantum chromodynamics\|QCD]] such as [[quarks]] or [[gluons]], or the more familiar electromagnetic charge if they are electrically charged [[leptons]] or [[quarks]], the most familiar charged [[lepton]] being the [[electron]] and since it is the lightest in [[mass]], the most numerous ~~due to the energy-time [[uncertainty principle]] as mentioned above; e.g., virtual electron–positron pairs. Such charged pairs act as an [[electric dipole]].~~ In the presence of an electric field, e.g., the [[electromagnetic field]] around an electron, these particle–antiparticle pairs reposition themselves, thus partially counteracting the field (a partial screening effect, a [[dielectric]] effect). The field therefore will be weaker than would be expected if the vacuum were completely empty. This reorientation of the short-lived particle-antiparticle pairs is referred to as '''vacuum polarization'''.

	~~The one-loop contribution of a fermion–antifermion pair to the vacuum polarization is represented by the following diagram:~~

	~~:[[Image:Vacuum polarization~~.~~svg]]~~

	~~== Vacuum polarization tensor ==~~

	~~The vacuum polarization is quantified by the vacuum polarization tensor Π~~<~~sup~~>μν<~~/sup~~>~~(p) which describes the dielectric effect as a function of the four~~-~~momentum p carried by the photon. Thus the vacuum polarization depends on the momentum transfer, or in other words, the [~~[dielectric constant]] is scale dependent. In particular, for electromagnetism we can write the [[fine structure constant]] as an effective momentum-transfer-dependent quantity; to first order in the corrections, we have

	:~~<math> \alpha_\text{eff}(p^2) = \frac{\alpha}{1 - [\Pi_2(p^2) - \Pi_2(0)]} </math>~~

	~~where Π<sup>μν<~~/~~sup>(p) = (p<sup>2</sup> g<sup>μν<~~/~~sup> - p<sup>μ</sup>p<sup>ν</sup>) Π(p<sup>2</sup>) and the subscript 2 denotes the leading order-e<sup>2</sup> correction~~. ~~The tensor structure of Π<sup>μν</sup>(p) is fixed by the [[Ward identity]]~~.

	~~==Note==~~
	Vacuum polarization affecting spin interactions has also been reported based on experimental data and also treated theoretically in [[Quantum chromodynamics\|QCD]], as for example in considering the [[hadron]] [[spin (physics)\|spin]] structure.

	=~~= See also ==~~
	* [[Renormalization]]
	* [[QED vacuum]]
	* [[QCD vacuum]]
	* [[Virtual particles]]

	~~== References ==~~
	~~<references~~ />

	~~== Further reading ==~~
	* For a derivation of the vacuum polarization in QED, see section 7.5 of M.E. Peskin and D.V. Schroeder, ''An Introduction to Quantum Field Theory'', Addison-Wesley, 1995.

	~~{{QED}}~~

	~~[[Category:Quantum field theory]]~~
	~~[[Category:Quantum electrodynamics]~~]

en>Monkbot: /* Maximum likelihood decoding */Fix CS1 deprecated date parameter errors

2014-01-16T12:53:12Z

Maximum likelihood decoding: Fix CS1 deprecated date parameter errors

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en>Sandeep.ps4: /* Maximum likelihood decoding */

2012-05-01T17:32:07Z

Maximum likelihood decoding

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