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Thursday, April 28, 2011

Micro-freedom and beyond

I read at:

http://en.wikipedia.org/wiki/Functional_renormalization_group

"Typically, low-energy physics of strongly interacting systems is described by macroscopic degrees of freedom (i.e. particle excitations) which are very different from microscopic high-energy degrees of freedom."

"For instance, quantum chromodynamics is a field theory of interacting quarks and gluons."

"At low energies, however, proper degrees of freedom are baryons and mesons."

"Another example is the BEC/BCS crossover problem in condensed matter physics."

"While the microscopic theory is defined in terms of two-component nonrelativistic fermions, at low energies a composite (particle-particle) dimer becomes an additional degree of freedom, and it is advisable to include it explicitly in the model."

"The low-energy composite degrees of freedom can be introduced in the description by the method of partial bosonization (Hubbard-Stratonovich transformation)."

"This transformation, however, is done once and for all at the UV scale Λ."

"In FRG a more efficient way to incorporate macroscopic degrees of freedom was introduced, which is known as flowing bosonization or rebosonization."

"With the help of a scale-dependent field transformation, this allows to perform the Hubbard-Stratonovich transformation continuously at all RG scales k."

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