The renormalization group (RG) is a mathematical and conceptual framework used in theoretical physics to study changes in a physical system as one looks at it at different scales. It is particularly prominent in quantum field theory, statistical mechanics, and condensed matter physics. The central idea behind the RG is that the properties of a system can change when one changes the scale at which one observes it.
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A Wilsonian renormalization-group step integrates out short-distance modes, rescales coordinates to restore the cutoff, and rescales fields to normalize a chosen kinetic term.
