Quantum Diffusion Process with a Complex Weight on Three Dimensional Lattice
Abstract
A rigorous definition of a path integral for a spinning particle in three dimensions is given on a regular cubic lattice. The critical diffusion constant and the associated critical exponents in each spin are calculated. Continuum field theories such as Klein-Gordon, Dirac and massive Chern-Simons theories are constructed near these critical points. The universality of obtained results is argued on some other lattices.
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