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In the context of Markov processes, we show a new scheme to derive dualprocesses and a duality function based on a boson representation. This schemeis applicable to a case in which a generator is expressed by boson creation andannihilation operators. For some stochastic processes, duality relations havebeen known, which connect continuous time Markov processes with discrete statespace and those with continuous state space. We clarify that using a generatingfunction approach and the Doi-Peliti method, a birth-death process (or discreterandom walk model) is naturally connected to a differential equation withcontinuous variables, which would be interpreted as a dual Markov process. Thekey point in the derivation is to use bosonic coherent states as a bra state,instead of a conventional projection state. As examples, we apply the scheme toa simple birth-coagulation process and a Brownian momentum process. Thegenerator of the Brownian momentum process is written by elements of theSU(1,1) algebra, and using a boson realization of SU(1,1) we show that the samescheme is available.

Duality in interacting particle systems and boson representation