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A new method for obtaining photoemission and other spectra is presented. The key idea is to expand transition amplitudes rather than the spectra themselves. This leads to spectral intensities of a Golden-rule-like form. In the language of Keldysh path-ordered technique, contributions to ''lesser'' functions such as G< are classified into loss and no-loss diagrams, and in each diagram transition amplitudes can be identified. Conserving theories in the sense of Kadanoff and Baym have the virtue of exact fulfillment of macroscopic conservation laws but may violate the positiveness of spectral functions. The present scheme may violate conserving laws but it will always give positive spectra. As such is is primarily suited for, say, photoemission and other spectra where the spectral shapes are of primary interest. As examples, we will discuss the one-electron spectral function beyond GW theory and in presence of phonons. In both cases we find subtle interference effects between self-consistency and vertex corrections and a marked improvent of satellites. As a final example, photoemission beyond the sudden approximation will be discussed. |