P(phi)2 models with variable coefficients

We study P(phi)2 models with variable coefficients on the nonlinear terms, for example, (D'Alembertian+m2)phi+rhophi3 = 0. Here rho is a function on spacetime usually of the form rho = rho0+rho1 with rho0 a positive constant and rho1 small and localized. For such models we construct solutions which satisfy the CCR, have a causal dependence on rho, and commute at spacelike separation. Asymptotic states and S-matrix elements are constructed when rho0 is also small. Finally, we study P(phi0)2 models on curved spacetime, for example (g/sup munu//sub μ/del/sub μ/del/sub ν/ +lambdaphi3 = 0, and indicate a construction of local solutions