“Dangerously irrelevant operator”的意思、由来-开放百科全书

词条

Dangerously irrelevant operator

释义

Example
References

In statistical mechanics and quantum field theory, a dangerously irrelevant operator (or dangerous irrelevant operator) is an 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.

Example

Let us suppose there is a field with a potential depending upon two parameters, and .

Let us also suppose that is positive and nonzero and > . If is zero, there is no stable equilibrium. If the scaling dimension of is , then the scaling dimension of is where is the number of dimensions. It is clear that if the scaling dimension of is negative, is an irrelevant parameter. However, the crucial point is, that the VEV

.

depends very sensitively upon , at least for small values of . Because the nature of infrared physics also depends upon the VEV, it looks very different even for a tiny change in not because the physics in the vicinity of changes much — it hardly changes at all — but because the VEV we are expanding about has changed enormously.

Supersymmetric models with a modulus can often have dangerously irrelevant parameters.

References

{{Cite journal | last1 = Amit | first1 = D. | last2 = Peliti | first2 = L. | title = On dangerous irrelevant operators | journal = Annals of Physics | volume = 140 | issue = 2 | pages = 207–231 | year = 1982 | doi = 10.1016/0003-4916(82)90159-2|bibcode = 1982AnPhy.140..207A | arxiv = cond-mat/0108323 }}{{DEFAULTSORT:Dangerously Irrelevant Operator}}{{Phys-stub}}

1 : Renormalization group

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