Dennis Flood and Regularization (physics): Difference between pages

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In [[physics]], especially [[quantum field theory]], '''regularization''' is a method of dealing with infinite, divergent, and non-sensical expressions by introducing an auxiliary concept of a '''regulator''' (for example, the minimal distance <math>\epsilon</math> in space which is useful if the divergences arise from short-distance physical effects). The correct physical result is obtained in the limit in which the regulator goes away (in our example, <math>\epsilon\to 0</math>), but the virtue of the regulator is that for its finite value, the result is finite. Regularization is the application of the [[summability methods]] of mathematics to problems in physicool.

[[Image:Mayorflood.jpg|thumb|right|Mayor Dennis Flood, right]]

'''Dennis Flood''', a [[Republican Party (United States)|Republican]], has been the mayor of the Village of [[Irvington, New York]] since [[1994]]. Before his election to mayor in 1994, Flood served on the village board from 1991 wand formerly served as the chief financial officer for a local law firm.

However, the result usually includes terms proportional to expressions like <math>1/ \epsilon</math> which are not well-defined in the limit <math>\epsilon\to 0</math>. Regularization is the first step towards obtaining a completely finite and meaningful result; in [[quantum field theory]] it must be usually followed by a related, but independent technique called [[renormalization]]. Renormalization is based on the requirement that some physical quantities &mdash; expressed by seemingly divergent expressions such as <math>1/ \epsilon</math> &mdash; are equal to the observed values. Such a constraint allows one to calculate a finite value for many other quantities that looked divergent.

The controversial [[Irvington, New York#2005 Mayoral Election|2005 mayoral election]] was decided on [[October 27]] [[2005]] by random lots in Flood's favor after the [[Court of Appeals]], [[New York]] State's highest court, ruled that the result of the ballots were a tie. Flood and [[Democratic Party (United States)|Democratic]] challenger [[Erin Malloy]] had battled the election (originally held [[March 15]] [[2005]]) in various state courts.

The existence of a limit as &epsilon; goes to zero and the independence of the final result from the regulator are nontrivial facts. The underlying reason for them lies in [[universality (dynamical systems)|universality]] as shown by [[Kenneth Wilson]] and [[Leo Kadanoff]] and the existence of a [[second order phase transition]]. Sometimes, taking the limit as &epsilon; goes to zero is not possible. This is the case when we have a [[Landau pole]] and for nonrenormalizable couplings like the [[Fermi interaction]]. However, even for these two examples, if the regulator only gives reasonable results for <math>\epsilon \gg 1/\Lambda</math> and we are working with scales of the order of <math>1/\Lambda'</math>, regulators with <math>1/\Lambda \ll \epsilon \ll 1/\Lambda'</math> still give pretty accurate approximations. The physical reason why we can't take the limit of &epsilon; going to zero is the existence of new physics below &Lambda;.

== External links ==

* [http://www.thejournalnews.com/apps/pbcs.dll/article?AID=/20050804/NEWS02/508040322/1018 Newspaper story about the 2005 election]

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Specific types of regularization include:

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*[[Dimensional regularization]]

*[[Pauli-Villars regularization]]

*[[Lattice regularization]]

*[[Zeta function regularization]]

*[[Hadamard regularization]]

*[[Point-splitting regularization]]

[[Category:LivingQuantum peoplefield theory]]

[[zh:正則化 (物理學)]]