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We have looked for evidence of large cross sections at large multiplicitiesin weakly coupled scalar field theory in three dimensions. We use spectralfunction sum rules to derive bounds on total cross sections where the sum canbe expresed in terms of a quantity which can be measured by Monte Carlosimulation in Euclidean space. We find that high multiplicity cross sectionsremain small for energies and multiplicities for which large effects had beensuggested.Comment: 23 pages, revtex, seven eps figures revised version: typos corrected,  some rewriting of discusion, same resul

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Nonperturbative bound on high multiplicity cross sections in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>theory in three dimensions from lattice simulation

Nonperturbative bound on high multiplicity cross sections inφ4theory in three dimensions from lattice simulation