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Physical Mathematics by Kevin Cahill

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19

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Strings

19.1 The infinities of quantum field theory

Quantum field theory is plagued with infinities. Even exactly soluble theories of free fields have ground-state energies that diverge quarticly, as +Λ4 for a theory of bosons and as −Λ4 for a theory of fermions as Λ → ∞. Theories with the same number of boson and fermion fields are less divergent, and theories with unbroken supersymmetry actually have ground-state energies that vanish.

One may be able to eliminate some of the infinities of a generic quantum field theory without spoiling the symmetries of its action density by replacing in the path integral by or . In euclidean space, the ...

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