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John R. Klauder
Nontrivial Quantization of phi-to-the-four for spacetime dimensions two and more
ABSTRACT. Conventional quantization of covariant scalar field models phi-to-the-four for spacetime dimensions five and more is trivial,
and this may also be true for four spacetime dimesions as well. However, an alternative order (hbar) counterterm leads to nontrivial results for all dimensions four and more, and provides a different quantization for dimensions two and three as well. In this article we determine the counterterm that provides these desirable properties as simply and directly as possible. The same counterterm also resolves models such as phi-to-the-p for all even p, including those where p greater than two n over (n minus two), which are traditionally regarded as nonrenormalizable.