It is used to convert a particle theory into its respective field theory by linearizing the density operator in the many-body interaction term of the Hamiltonian and introducing a scalar auxiliary field. It is defined as (Baeurle 2002, Baeurle 2003)
where the real constant a > 0. The basic idea of the HS transformation is to reformulate a system of particles interacting through two-body potentials into a system of independent particles interacting with a fluctuating field.
— Wikipedia on Hubbard-Stratonovich transformation
2009.12.20 Sunday ACHK