Interactions in Infinite Dimensions

Simon Brian Davis


The noncommuting variables of quantum theory find a theoretical basis in an
infinite-dimensional classical formalism.  The connection between theories of objects with dimension and classical point-particle models is clarified.  It is demonstrated that the interaction region in the reduction of scattering amplitudes in quantum field theory is restricted to a region of a radius that scales as $d^{1\over 2}$ in
$d$ dimensions.  The existence of a mass gap for a scalar field in the massless limit
in the interior of a finite interaction region is proven when there are no bound state diagrams.  

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