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Physical Mathematics by Kevin Cahill

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17

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The renormalization group

17.1 The renormalization group in quantum field theory

Most quantum field theories are nonlinear with infinitely many degrees of freedom and, because they describe point particles, they are rife with infinities. But short-distance effects, probably the finite sizes of the fundamental constituents of matter, mitigate these infinities so that we can cope with them consistently without knowing what happens at very short distances and very high energies. This procedure is called renormalization.

For instance, in the theory described by the Lagrange density

(17.1)

we can cut off divergent integrals at some high ...

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