Abstract:
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.
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