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We report on the status of the string-inspired world line path integral formalism, a recently developed powerful tool for the reorganisation of standard perturbative amplitudes in quantum field theory. The method is outlined and the present range of its applicability surveyed. The emphasis is on QED and QCD photon/gluon amplitudes, with a short discussion of axial couplings.

In the past chapter we gave a summary of the Hilbert space picture of Quantum Mechanics and of a Scalar Quantum Field Theory. Here we will present the Path Integral picture of Quantum Mechanics and Scalar Quantum Field Theory.

For thermal equilibrium systems it is shown, how the Kubo-Martin-Schwinger boundary condition may be used to factorize the generating functional of Green functions at least on the level of the full two-point function. Genuine non-equilibrium system exhibit correlations that one may also incorporate in the path integral. One one hand this provides a natural tool for a perturbative expansion including these correlations. On the other hand it allows to prove that in general non-equilibrium systems the generating functional does not factorize.