Physics
Scientific paper
Feb 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005tmgm.meet..224k&link_type=abstract
The Tenth Marcel Grossmann Meeting. Proceedings of the MG10 Meeting held at Brazilian Center for Research in Physics (CBPF), Rio
Physics
Scientific paper
From a functional integral viewpoint, it is characteristic of nonrenormalizable quantum theories that the nonlinear interaction is sufficiently singular that it forbids certain field histories that would otherwise be allowed by the noninteracting theory alone. Since such forbidden field histories are projected out of the functional integral no matter how small the coupling constant - exactly like a hard-core potential would behave - the interacting theory is not even continuously connected to the noninteracting theory as the coupling constant vanishes. Although, regularization and expansion of the interaction in a perturbation series is invariably inappropriate, alternative procedures have been difficult to formulate. Recent schemes for dealing with quartically coupled scalar fields in spacetime dimensions greater than four are presented, and arguments are even given to indicate that they may also be used to overcome triviality in four spacetime dimensions. Possible implications for quantum gravity are also mentioned.
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