RGApproachToInteractingFermions: Difference between revisions
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The basic proceedure is as follows. Let us consider a given interacting Hamiltonian, and write the associated partition function in path integral form: | The basic proceedure is as follows. Let us consider a given interacting Hamiltonian, and write the associated partition function in path integral form: | ||
<math>Z=\int{D[\psi^{\ast},\psi] e^{-S[\psi^{\ast},\psi]},</math> | <math> \displaystyle Z=\int{D[\psi^{\ast},\psi] e^{-S[\psi^{\ast},\psi]}},</math> | ||
where the action <math>S</math> is | where the action <math>S</math> is | ||
Revision as of 14:49, 30 November 2010
Introduction
The renormalization group (RG) is a very powerful tool in physics. Essentially, it is a way to continuously map a given theory onto other theories possessing the same low-energy physics by successively integrating out "fast", or high-energy, modes. This is expressed in terms of differential equations giving the "flows" of different coupling constants that appear in the theory.
The basic proceedure is as follows. Let us consider a given interacting Hamiltonian, and write the associated partition function in path integral form:
![{\displaystyle \displaystyle Z=\int {D[\psi ^{\ast },\psi ]e^{-S[\psi ^{\ast },\psi ]}},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2c2d2c322584032e130002c12b073a1b7c76076a)
where the action is
