RGApproachToInteractingFermions: Difference between revisions
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=Introduction= | =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: | |||
<math>Z=\int{D[\psi^{\ast},\psi] e^{-S[\psi^{\ast},\psi]},</math> | |||
where the action <math>S</math> is | |||
=System at half-filling in one dimension= | =System at half-filling in one dimension= | ||
Revision as of 14:47, 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:
Failed to parse (syntax error): {\displaystyle Z=\int{D[\psi^{\ast},\psi] e^{-S[\psi^{\ast},\psi]},}
where the action is
