Editing Renormalization (section)

===Principles===
In more technical terms, let us assume that we have a theory described
by a certain function <math>Z</math> of the state variables
<math>\{s_i\}</math> and a certain set of coupling constants
<math>\{J_k\}</math>. This function may be a [[partition function (quantum field theory)|partition function]],
an [[Action (physics)|action]], a [[Hamiltonian (quantum mechanics)|Hamiltonian]], etc. It must contain the
whole description of the physics of the system.

Now we consider a certain blocking transformation of the state
variables <math>\{s_i\}\to \{\tilde s_i\}</math>,
the number of <math>\tilde s_i</math> must be lower than the number of
<math>s_i</math>. Now let us try to rewrite the <math>Z</math>
function ''only'' in terms of the <math>\tilde s_i</math>. If this is achievable by a
certain change in the parameters, <math>\{J_k\}\to
\{\tilde J_k\}</math>, then the theory is said to be
'''renormalizable'''.

The possible
macroscopic states of the system, at a large scale, are given by this
set of fixed points.