Stochastic bosonization in arbitrary dimensions

Accardi, L.; Lu, Y. G.; Volovich, I.

Stochastic bosonization in arbitrary dimensions

Authors

Accardi, L.

Lu, Y. G.

Volovich, I.

Description

A procedure of bosonization of Fermions in an arbitrary dimension is suggested. It is shown that a quadratic expression in the fermionic fields after rescaling time $t\to t/λ^2$ and performing the limit $λ\to0$ (stochastic limit), gives rise to a bosonic operator satisfying the boson canonical commutation relations. This stochastic bosonization of Fermions is considered first for free fields and then for a model with three--linear couplings. The limiting dynamics of the bosonic theory turns out to be described by means of a quantum stochastic differential equations.
14 pages, Tex