A Path Integral Approach to Inclusive Processes

The single-particle inclusive differential cross-section for a reaction $a+b\to c+X$ is written as the imaginary part of a correlation function in a for ward scattering amplitude for $a+b\to a+b$ in a modified effective theory. In this modified theory the interaction Hamiltonian ${\tilde{H}}_I$ equals $H_I$ in the original theory up to a certain time. Then there is a sign change and ${\tilde{H}}_I$ becomes nonlocal. This is worked out in detail for scalar field models and for QED plus the abelian gluon model. A suitable path integral for direct calculations of inclusive cross sections is presented.