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| {{refimprove|date=November 2010}}
| | Friends call him Royal Cummins. Bookkeeping is what she does. Some time in the past he selected to reside in Kansas. Her friends say it's not great for her but what she loves performing is flower arranging and she is trying to make it a profession.<br><br>My site: [http://Kstyle3.sakura.ne.jp/apparels/5864754 http://Kstyle3.sakura.ne.jp/apparels/5864754] |
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| In [[statistical mechanics]] and [[quantum field theory]], a '''dangerously irrelevant operator''' (or '''dangerous irrelevant operator''') is an [[operator (mathematics)|operator]] which is irrelevant, yet affects the [[infrared]] (IR) physics significantly because the [[vacuum expectation value]] (VEV) of some field depends sensitively upon the operator.
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| ==Example==
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| Let us suppose there is a field <math>\phi</math> with a [[potential]] depending upon two parameters, ''a'' and ''b''.
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| :<math>V\left(\phi\right)=-a \phi^\alpha + b\phi^\beta</math> | |
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| Let us also suppose that ''a'' is positive and nonzero and <math>\beta</math> > <math>\alpha</math>. If ''b'' is zero, there is no stable equilibrium. If the [[scaling dimension]] of <math>\phi</math> is ''c'', then the scaling dimension of ''b'' is <math>d-\beta c</math> where ''d'' is the number of dimensions. It is clear that if the scaling dimension of ''b'' is negative, ''b'' is an irrelevant parameter. However, the crucial point is, that the VEV
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| :<math>\langle\phi\rangle=\left(\frac{a\alpha}{b\beta}\right)^{\frac{1}{\beta-\alpha}}=\left(\frac{a\alpha}{\beta}\right)^{\frac{1}{\beta-\alpha}}b^{-\frac{1}{\beta-\alpha}}</math>. | |
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| depends very sensitively upon ''b'', at least for small values of ''b''. Because the nature of infrared physics also depends upon the VEV, it looks very different even for a tiny change in ''b'' not because the physics in the vicinity of <math>\phi=0</math> changes much — it hardly changes at all — but because the VEV we are expanding about has changed enormously.
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| [[supersymmetry|Supersymmetric]] models with [[moduli space|a modulus]] can often have dangerously irrelevant parameters.
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| ==References==
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| {{cite doi|10.1016/0003-4916(82)90159-2}}
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| {{DEFAULTSORT:Dangerously Irrelevant Operator}}
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| [[Category:Renormalization group]]
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| {{Phys-stub}}
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Latest revision as of 21:22, 19 November 2014
Friends call him Royal Cummins. Bookkeeping is what she does. Some time in the past he selected to reside in Kansas. Her friends say it's not great for her but what she loves performing is flower arranging and she is trying to make it a profession.
My site: http://Kstyle3.sakura.ne.jp/apparels/5864754