Dynamical theory of the vacuum

An $S$ matrix theory is constructed inwhichthe “free Lagrangian” $L_0$ may have a complicated structure. The Lagrangian $L_0$ determines the properties of the vacuum, which are described by Green's functions. Scattering is due to the interaction Lagrangian $L_\mathrm{int}$. If $L_\mathrm{int}=0$, then $S=1$, i.e., there is no scattering. A functional method is developed to determine the Green's functions and the $S$ matrix. This method yields an expansion of the $S$ matrix in powers of the function $\varphi (x)$. The coefficients of this expansion are scattering amplitudes. A generalized diagram technique is constructed to calculate the $S$ matrix. It is shown that if certain assumptions concerning the Lagrangian $L_0$ and $L_\mathrm{int}$ are made the $S$ matrix is unitary. and causal. Some physical applications of the theory are discussed.